NEW ORLEANS (AP) _ Although the State Department says it considers the case of Miroslav Medvid closed, a Ukrainian-American family arrived from Ohio on Sunday trying to prevent the sailor's return to the Soviet Union.

The State Department says the Soviet seaman had ample opportunity to defect but did not ask for asylum when he was interviewed on shore last week.

Medvid leaped twice into the Mississippi from the freighter Marshal Koniev, but was put back aboard by U.S. authorities before being interviewed on shore at the insistence of the State Department. After the interview, he returned to the ship.

However, various anti-Soviet and pro-Ukrainian groups dispute that Medvid really wants to return to the Soviet Union.

Members of a Parma, Ohio, family who say they may be related to Medvid arrived in New Orleans to prevent Medvid's return to the Soviet Union.

Paraska Jeziersky, whose maiden name was Medvid, arrived with her daughters, Anne Kent and Mary Filipovich, and Mrs. Jeziersky's husband, Tom. Mrs. Jeziersky said she learned from media reports that Medvid comes from a part of the Ukraine ''close to where I come from.''

When the women were asked about the possibility that Medvid was not related to them, Ms. Filipovich replied, ''If that's that case, let the Russians prove he's not related to us.''

The group was met at the airport by Phoenix attorney Orest Jejna, who identified himself as a member of the board of directors of the Ukrainian- American Bar Association. Jejna said he was seeking to represent Medvid.

''Undisputedly, Miroslav Medvid wanted to stay. He had his watch and legal papers in a jar,''Jejna said.

Also arriving in New Orleans on a separate flight Sunday was Jeff Pandin, a representative of a group calling itself the Save The Oppressed People Committee. Pandin said he planned to organize a flotilla to prevent the Soviet freighter from leaving a grain elevator in Reserve, La.

''What we're shooting for right now is a number of large rubber rafts and a large boat that we can put reporters on,'' he said. ''We're also issuing a call for everyone and anyone with a boat in southeast Lousiana to join us.''

''Our hope is to prevent the ship from leaving, or at least to slow it down so that the legal process can catch up with us,'' Pandin said.

''Our biggest concern is that they (the Soviets) are going to squeak out of here before the legal wheels can turn, or the Justice Department can reopen the case,'' he said.

Also Sunday, a congressman said that sailors aboard the freighter told an American minister and two others that Medvid intended to defect when he twice jumped from the ship.

Rep. Don Ritter, D-Pa., said an affidavit detailing the conversation between the minister and two others in a small launch and sailors aboard the freighter would be filed as part of a case pending in federal court to prevent the ship from leaving U.S. waters before Medvid is interviewed again.

A decision was expected from the U.S. Circuit Court of Appeals in the District of Columbia soon, possibly as early as Monday, on Ukrainian-America n groups' appeal of a district judge's refusal to forbid the ship from leaving a grain elevator in Reserve.