(CNN) The St. Louis circuit attorney's office has publicly criticized police, saying they obstructed an investigation into last week's fatal shooting of an officer and prematurely labeled it an accident.

In a letter Monday to St. Louis Metropolitan Police Commissioner John Hayden and Public Safety Director Jimmie Edwards, Circuit Attorney Kimberly M. Gardner wrote there was probable cause that drugs or alcohol may have been a contributing factor in the shooting of Katlyn Alix, a 24-year-old police officer.

Officer Nathaniel Hendren, 29, fatally shot Alix at his residence Thursday after the two allegedly took turns holding a revolver containing one bullet and pulling the trigger, according to police. The lethal game of chance is sometimes known as Russian roulette.

Hendren has been charged with involuntary manslaughter in the first degree and armed criminal action relating to the death of a fellow police officer.

Despite the existence of probable cause, Gardner wrote that prosecutors were not allowed to take a blood test of Hendren and an unnamed on-duty officer also present. They were later informed that a urine analysis and a breath test, which are less exact than a blood test, had been taken under Garrity rights . These are warnings that public employees have a right to remain silent.

Nathaniel Hendren faces an involuntary manslaughter in the first degree charge.

"Taking these tests under the cover of Garrity appears as an obstructionist tactic to prevent us from understanding the state of the officers during the commission of this alleged crime," Gardner wrote in the letter.

The circuit attorney said that police initially told investigators that the shooting was an "accident," and also characterized it as a "mishandling" of a firearm.

Gardner's letter called such conclusions troubling.

"In my opinion, it is completely inappropriate for investigators to approach a crime scene that early in the investigation with a pre-disposed conclusion about the potential outcome of a case," she wrote. "It's particularly troublesome given that the Force Investigative Unit is required to conduct objective investigations of officer-involved shootings.

"I understand your need to get information out to the public quickly regarding officer-involved shooting cases, however, the labeling of any criminal incident as an accident prior to a full investigation is a violation of our duty as objective fact finders."

Gardner's office said it is conducting an independent investigation of the shooting, and the Missouri State Highway Patrol will assist.

Police did not immediately respond to CNN's requests for comment.

Susan Ryan, spokeswoman for the circuit attorney's office, said police and her department have a good relationship overall despite this issue.

"The relationship with the police department and prosecutors has a natural tension because of the checks and balances that we have to do regarding their work," Ryan said.

Defense attorney says shooting was an accident

The sternly worded letter raises more questions about the case and comes days after Hendren's attorney described it as nothing more than an accident.

"We are aware of the rumors, innuendo, and salacious gossip surrounding the accidental death of Officer Katlyn Alix," attorney Talmage E. Newton IV said. "There is no evidence, nor will there ever be, that this was anything more than a tragic accident."

Alix was off duty at the time of last week's shooting, and Hendren was on duty, according to a probable cause statement supporting the charges.

The statement said Alix, Hendren and Hendren's partner were playing with guns when Hendren produced a revolver. Hendren emptied the bullets from the revolver and put one of the bullets back inside the gun, spun the cylinder and fired the gun pointing away from Alix, the statement said. The gun did not discharge.

Alix took the gun and pulled the trigger while pointing at Hendren, but it did not fire, the statement said. Hendren grabbed the gun back from Alix, pulled the trigger, and this time it fired, striking Alix in the chest, the document said. She was taken to the hospital and was pronounced dead shortly after arrival.

The third officer at the scene has not been identified. According to the probable cause statement, he advised Alix and Hendren they shouldn't be playing with guns and left the room. He returned after hearing the gunshot.

Hendren was taken into custody Monday, and a booking photo shows him with a black eye.

In first reporting the shooting, police said the death was accidental and occurred when an unnamed officer "mishandled" a gun while they were sitting in the living room.

Alix had been on the force two years, the police department said. She leaves behind a husband, her parents and a sister, among other family members.

Her family has hired attorney Scott Rosenblum.

"I've been retained by the Alix family to make sure that the investigation is thorough and proper," Rosenblum said. "We will obviously explore if there are any civil remedies that they can pursue. Right now, their primary concern is making sure the investigation is thorough and proper."