His fellow Republicans including House Speaker Kevin McCarthy have accused Bragg, a Democrat, of abuse of power and using his office to pursue a political agenda.
McCarthy had also said he would direct House committees to determine whether federal funds have been used in the district attorney's probe.
The letter was signed by House Judiciary Committee Chairman Jim Jordan, House Oversight Committee Chairman James Comer and House Administration Committee Chairman Bryan Steil.
"Congress has no jurisdiction to investigate the Manhattan DA, which receives no federal funding nor has any other federal nexus," added Goldman, who was lead counsel in a 2019 House impeachment of Trump.
Trump, who is seeking the 2024 Republican presidential nomination, has said he would continue campaigning even if charged with a crime.