MOSCOW — After shopping around for a defense lawyer this year, a Russian state bank settled on someone who it said had relevant experience, though the bank insists that experience does not include a promotional pitch from the lawyer’s firm: representing “President Donald J. Trump in a wide range of litigation matters for over 15 years.”

In Russia, finding the right insider connection is essential for litigation success, but the case against the bank, Sberbank, is playing out in Federal District Court in Manhattan. There, concerns have been raised about Sberbank’s reasons for hiring the lawyer, Marc E. Kasowitz, as its lead defense counsel. The bank is being sued by a Russian businessman, Sergey P. Poymanov, who has sparred with it for years in Russian courts.

The lawsuit appears unrelated to another of Mr. Kasowitz’s cases involving Russia — defending Mr. Trump in an investigation into possible collusion by his campaign officials in Russia’s meddling in last year’s presidential election. Mr. Kasowitz had been introduced as the lead lawyer in that matter, too, but his responsibilities have since been scaled back, and a lawyer with more Washington experience, Ty Cobb, has taken the lead.

The potential for Russia’s meddling elsewhere — in American courts — has raised concerns among Mr. Poymanov’s lawyers, who are not convinced that Mr. Kasowitz’s ties to Mr. Trump played no role in Sberbank’s choosing him. They point out that on its website, Mr. Kasowitz’s firm, Kasowitz Benson Torres, prominently advertises his 15 years of pre-election service to the president.