By Mark Maremont and Nick Kostov

BOSTON -- Carlos Ghosn wired more than $860,000 to a company tied to one of the two men being held in the U.S. on suspicion that they helped the former auto titan escape from Japan late last year, according to new court documents introduced by federal prosecutors.

The new documents come as the two men, a Massachusetts father and son, filed a fresh lawsuit seeking to be released on bail as they battle extradition to Japan for their alleged roles in the escape.

Michael L. Taylor, 59 years old, and his son Peter M. Taylor, 27, argued that they should be released on bail due in part to an outbreak of Covid-19 at the county jail where they are being held pending extradition. Thirty-six inmates at the county jail had tested positive for Covid-19 as of July 2, and one inmate died on that date, according to the new complaint, filed this week in U.S. District Court in Massachusetts.

Mr. Ghosn, who was living in a court-monitored Tokyo house while facing financial-crime allegations from his time running Nissan Motor Co., fled Japan late last year, smuggled inside a musical-equipment box onto a waiting private jet. U.S. prosecutors said the Taylors were key participants in the plot, citing the Japanese investigation which included extensive video evidence of their movements in Japan.

Mr. Ghosn has denied the financial-crimes allegations in Japan and has said he fled the country because he wouldn't receive a fair trial.

Michael Taylor is a longtime security operative and former Army Special Forces soldier who has made a career out of arranging complicated overseas rescues and other missions. He and his son were arrested in the U.S. on May 20 by federal authorities, acting at the request of Japanese officials.

The bank documents filed by U.S. prosecutors on Tuesday are the first allegedly demonstrating direct financial ties between Mr. Ghosn and the Taylors.

The documents showed two wire transfers in October 2019 totaling $862,500 from a Paris bank account prosecutors said was connected with Mr. Ghosn, to Promote Fox LLC, a limited-liability company managed by Peter Taylor and one of his brothers.

The wire-transfer records were included in a formal extradition request made by Japanese authorities for the Taylors, parts of which were introduced into court records this week. A spokeswoman for Mr. Ghosn and an attorney for the Taylors declined to comment on the wire transfers.

It isn't clear how much, if anything, the Taylors were paid by Mr. Ghosn to help with the escape. Expenses for the plot included the charter of two private jets. One jet, according to Japanese prosecutors, flew Michael Taylor and an associate from Dubai to Japan, where they allegedly loaded the box containing Mr. Ghosn through a cargo door.

That jet flew to Istanbul, where Mr. Ghosn transferred to a second jet bound for Lebanon, which has no extradition treaty with Japan.

The Taylors have hired a high-profile legal team to battle the extradition request, including Abbe Lowell, who has represented Jared Kushner and Ivanka Trump. Their lawyers have argued the father and son didn't commit a crime in Japan and in any case should be released on bail pending a decision on whether to extradite them.

Federal Magistrate Judge Donald L. Cabell on Tuesday rejected the Taylors' motions filed early last month to quash their arrest warrants. Judge Cabell as of Tuesday afternoon hadn't yet ruled on the Taylors' request to be released on bail.

The Taylors' new lawsuit cited the length of time it was taking Judge Cabell to rule on the bail request, saying it "allowed the Taylors' improper deprivation of liberty under life threatening conditions to continue."

Write to Mark Maremont at mark.maremont@wsj.com and Nick Kostov at Nick.Kostov@wsj.com