There was an inquiry. It convened in Chicago, IL in early 1879. It was an inquiry into Maj. Marcus Reno's conduct during the battle (at his request). After extensive testimony he was exonerated from wrongdoing, although it also didn't find favor in his conduct. He left military service after a couple courts martial for behavior unbecoming an officer.
Reno definitely had a drinking problem (so did Capt. William Benteen, as well as many in the military at that time). Much of the animosity toward Reno stemmed from charges of his drinking before or during the engagement, although that was never proven.
Hello
about the Reno Court of Inquiry, which was made AFTER some people questioned Benteen and Reno, see:
Weir died of 'consumption' soon after the battle. If anyone ever got a glimpse of Custer's demise... it was either him or Edgerly.