East Hampton Town Police were still searching on Tuesday for the bodies of two victims and the majority of the wreckage of a private plane that crashed about a mile off Indian Wells Beach in Amagansett on Saturday, killing a prominent East Hampton couple, their grandson and the pilot.The Piper Navajo PA 31—carrying Bernard “Ben” Krupinski, 70, and his wife, Bonnie Krupinski, 70; their grandson, William Maerov, 22; and pilot Jon Dollard of Hampton Bays, 47—left Newport State Airport in Rhode Island at approximately 2 p.m., according to a representative from the airport who declined to be identified by name. The National Transportation Safety Board is still investigating what caused the crash.In an email on Monday, Terry Williams, a public affairs officer with the NTSB, the lead agency in charge of the investigation, estimated that it could be a year or more before an analysis would be completed to determine the cause of the crash. However, a preliminary report is expected in about a week.“We are in the early stages of this investigation and gathering information,” Mr. Williams said. An official of the airport in Newport, Rhode Island, said a second plane, also owned by the Krupinskis, took off from the Rhode Island airport and is believed to have successfully landed at East Hampton Airport: “One landed and one didn’t.” Police have not confirmed who was aboard the second plane or when it arrived.Watchstanders at U.S. Coast Guard Sector Long Island Sound received a call from East Hampton Airport at approximately 2:50 p.m. on Saturday reporting a plane had crashed into the ocean. The East Hampton Town Lifeguards recovered two bodies shortly after the crash on Saturday; the identities have not yet been released by police. As of Tuesday afternoon, most of the plane’s wreckage and its two remaining occupants have not been found.On Tuesday, East Hampton Town Police Chief Michael Sarlo suggested to the Town Board that parts of the plane might still be intact, and that Sea Tow, a Hampton Bays-based maritime assistance company working for the plane’s insurer, likely would be enlisted to raise any wreckage that is located. Chief Sarlo said investigators are mapping out the general location where the Piper Navajo is thought to have crashed, using data about the wreckage from vessels that were on the scene on Saturday afternoon.“We hope to … shrink down the search area and, hopefully, pinpoint where the wreckage is,” Chief Sarlo said. “And we’re hoping to be able to recover the other two missing victims.” He had said earlier that search operations now are recovery efforts; hopes of rescuing possible survivors ended on Sunday. Police confirmed that the plane had lost contact with East Hampton Airport about a mile south of the coast just as a strong thunderstorm crossed the South Fork on Saturday afternoon. Boaters had located a debris field off Indian Wells Beach a short time later.David Aripotch, the captain of the Montauk-based fishing boat Caitlin & Mairead, which was one of the first vessels on the scene of Saturday’s crash, said that the strong squall had blown through right before reports of the crash. “The weather was awful savage,” Mr. Aripotch said. “There wasn’t a lot of wind, but there was a lot of rain and lightning—a lot of lightning. It went by quick and, right after that, the Coast Guard came on [the radio] and said there was a plane crash. We were four to five miles east, so we headed there. Right after we got there, we heard them say they had found [a body].” When reached on Saturday, Ryan O’Hare of Coast Guard Station Montauk said that the plane had reportedly crashed around the time that thunderstorms had entered the area. “I can’t confirm that was the cause,” he said. The Newport airport representative confirmed that Mr. Krupinski did not purchase fuel for either of the aircrafts prior to taking off, and that neither of the planes’ pilots had filed a flight plan.On Sunday, the U.S. Coast Guard and East Hampton Town Police temporarily suspended the search for the wreckage and the Navajo’s remaining passengers due to “rapidly deteriorating sea conditions.”Coast Guard spokeswoman Lieutenant Alaina Fagan added that patrol boats had reported 25-knot winds and 6-foot seas on Sunday—an increase from 6-knot winds and 1-foot seas on Saturday.“This is always a difficult decision, and we cannot imagine the pain of those families who have lost their loved ones,” the Coast Guard said of the suspended search in a press release on Sunday.“We are confident, based on our search efforts, that we’ve looked extensively at the debris areas and where it had traveled. We are confident that if the missing people were on the surface of the water, we would have found them,” Lt. Fagan added.While assets—including the Air National Guard, East Hampton Police Dive Team, East Hampton Ocean Rescue Squad, and commercial fishing boats such as the Caitlin & Mairead, owned by David Aripotch, and Sea Tow, owned by Les Trafford—suspended their search, law enforcement officials, including the Southampton Town bay constables, East Hampton Town Marine Patrol and State Police, continued to patrol the beaches between East Hampton and Southampton Village. “It was quite the horrific scene,” said Douglas Davidson, a crew member on the Caitlin & Mairead. “There was a lot of debris. Socks, shoes, lots of clothing. The seats of the plane were floating. We picked up a purse. It was bad.” The search remained suspended throughout Monday into Tuesday morning, when East Hampton Town Police said they would launch at least one vessel in search of the bodies of the remaining passengers.The town’s search had been kept at bay since early Sunday morning, because of high winds and rough seas. On Tuesday morning, Chief Sarlo said that the renewed search effort was expected to be brief, as the region was expected to be hit with high winds and thunderstorms later in the day. He hoped for better conditions on Wednesday and Thursday to resume the search.“It’s still very choppy and a pretty good sweep to the west, so it’s difficult conditions for us to deploy the side-scan sonar and submersibles, and it’s not safe for divers to go down yet,” Chief Sarlo told the East Hampton Town Board on Tuesday, though he added that police are still conducting around-the-clock patrols of the ocean beaches between Amagansett and Southampton in search of debris, which has been spread west by two days of strong easterly winds.Chief Sarlo also said that commercial fishermen have been asked not to drag nets or drop fishing lines in the general vicinity of the crash, and that residents have been asked to call the police immediately if they spot any debris potentially related to the crash on local beaches. The chief offered the condolences of his department to the families that lost loved ones in the crash. “The Krupinskis and Bistrians were a major part of our community and were extremely supportive of all of us first responders in the community,” he said, referring to Ms. Krupinski’s family. The chief and members of the Town Board also thanked emergency responders from the Town Police, Marine Patrol, Ocean Rescue, East Hampton Lifeguards, East Hampton Village, Southampton Town, the U.S. Coast Guard, the U.S. Air National Guard, the Suffolk County Sheriffs office, Suffolk County Police and State Police for the help in Saturday’s search efforts. “Everyone deserves high praise under what were very difficult circumstances,” Supervisor Peter Van Scoyoc said.Senior staff writer Michael Wright contributed to this story.