WASHINGTON — The Constitution does not answer every question. It includes detailed instructions, for instance, about how Congress may remove a president who has committed serious offenses. But it does not say whether the president may be criminally prosecuted in the meantime.

The Supreme Court has never answered that question, either. It heard arguments on the issue in 1974 in a case in which it ordered President Richard M. Nixon to turn over tape recordings, but it did not resolve it.

Reports that President Trump asked James B. Comey, then the F.B.I. director, to shut down an investigation into his former national security adviser, Michael T. Flynn, prompted accusations that the president may have obstructed justice. Robert S. Mueller III, the former F.B.I. director who has been appointed special counsel to look into ties between the Trump campaign and Russia, will presumably investigate the matter.

But would the Constitution allow Mr. Mueller to indict Mr. Trump if he finds evidence of criminal conduct?