Attorney General Eric T. Schneiderman of New York is moving to change New York state law so that he and other local prosecutors would have the power to bring criminal charges against aides to President Trump who have been pardoned, according to a letter Mr. Schneiderman sent to the governor and state lawmakers on Wednesday.

The move, if approved by Gov. Andrew M. Cuomo and the Legislature, would serve notice that the legal troubles of the president and his aides may continue without the efforts of Robert S. Mueller III, the special counsel investigating possible Russian interference in the 2016 presidential election.

Under the plan, Mr. Schneiderman, a Democrat, seeks to exempt New York’s double jeopardy law from cases involving presidential pardons, according to the letter, a copy of which was obtained by The New York Times. The current law and the concept of double jeopardy in general mean that a person cannot be tried for the same crime twice.

Right now, New York state law prevents people from being prosecuted more than once for crimes related to the same act, even if the original prosecution was in federal court. There are already a number of exceptions to the law, and the letter says that Mr. Schneiderman is proposing to add a new one that could be used if federal pardons are issued.