(CNN) -- The American Civil Liberties Union has called on officials in Massachusetts and Florida to conduct independent investigations into the shooting death of a man by an FBI agent.

Ibragim Todashev was fatally shot early May 22 during questioning about a 2011 triple homicide in Waltham, Massachusetts, as well as his relationship with deceased Boston Marathon bombing suspect Tamerlan Tsarnaev.

Law enforcement from Massachusetts and Florida as well as the FBI questioned Todashev at his Florida home.

Details about the circumstances of Todashev's death have been few, and the gaps have been filled in by media reports quoting unnamed law enforcement sources.

The reports have raised the question about how much of a threat Todashev posed before being shot.

The FBI is conducting an investigation into the shooting, but the ACLU said that action is not enough.

"Florida officials are simply deferring to the FBI, allowing the FBI to investigate itself, but it is difficult to accept the FBI's honesty in this matter," Howard Simon, ACLU of Florida's executive director, said in a statement Monday.

"The FBI has offered completely incompatible explanations; they have failed to explain how these inconsistent stories found their way into newspaper accounts of the shootings, and have not offered any clarifying comment about what really happened."

The rights group sent a letter to Massachusetts Attorney General Martha Coakley asking her office to investigate the role of officers from her state in the shooting. In Florida, the ACLU asked the Florida Department of Law Enforcement to investigate the role of Orlando police at the scene.

A U.S. government official briefed on the FBI investigation told CNN in May that Todashev had agreed to talk to authorities and noted he was never arrested or handcuffed.

A samurai sword was in the room when Todashev sat down with two Massachusetts State Police detectives and a Boston-based FBI agent, but it was moved out of his reach, the U.S. official said.

After one of the detectives left the room, the other noticed Todashev was acting odd, and he texted that sense to the FBI agent with him -- the U.S. official told CNN. Those two law enforcement officials were the only ones with Todashev, according to this account.

Suddenly, Todashev knocked over a table -- knocking the FBI agent back into a wall -- and came at him with some sort of "long-handled object" that he'd grabbed from behind him, according to the official.

The agent fired a few rounds, but Todashev kept on coming, the official said. He finally stopped after yet more gunshots.

A law enforcement official told CNN that Todashev attacked the FBI agent with a broom handle, not a sword.