With the Justice Department on Monday ordering federal prosecutors in Manhattan to drop corruption charges against Mayor Eric Adams of New York, the legal spotlight could shift to a local prosecutor — the Manhattan district attorney’s office, and its leader, Alvin L. Bragg.

Mr. Adams was indicted on five counts of bribery conspiracy, fraud and soliciting illegal foreign campaign donations. The order by Emil Bove III, the Justice Department’s acting No. 2 official, did not clear Mr. Adams of wrongdoing. Mr. Bove said he had not assessed “the strength of the evidence.”

The memo to federal prosecutors said there was to be “no further targeting of Mayor Adams or additional investigative steps” until after the November mayoral election, when the case could be re-evaluated.

But while Mr. Bragg has shown that he is willing to tangle with the president and his allies — he won a criminal conviction of Mr. Trump on 34 felony counts last year — he or any other prosecutor would face daunting obstacles in building a case against the mayor.

It would be “highly unusual” for the Manhattan district attorney’s office to begin its own investigation into Mr. Adams at this point, but nothing would prevent it if the statutes of limitations for any state crimes have not run out, said Cyrus R. Vance Jr., Mr. Bragg’s predecessor.

With the cooperation of federal prosecutors — which would mean access to federal witness interviews, grand jury statements and subpoenaed documents — Mr. Bragg would be able to pull together a case quickly, Mr. Vance said. But given that Mr. Trump’s Justice Department is highly unlikely to provide that cooperation, the office would have to “essentially rebuild the case from the ground up,” Mr. Vance said.