FALL RIVER, Mass. — Prosecutors in the murder trial of former New England Patriots tight end Aaron Hernandez asked the judge Monday to let them tell jurors about his involvement in a friend’s shooting in Florida, saying it contradicts the argument his defense team has presented: that he would not shoot a friend.

Superior Court Judge Susan Garsh ruled in December that prosecutors could not introduce evidence about the February 2013 shooting of Alexander Bradley during Hernandez’s murder trial. Hernandez is charged with killing Odin Lloyd, who was dating the sister of Hernandez’s fiancee, in June 2013 in an industrial park near Hernandez’s home.

In papers filed Monday, prosecutors argued that the judge should reconsider. They wrote that Hernandez’s defense team is intentionally distorting the facts and introduced “a falsehood” to the jury. They said Hernandez’s defense had opened the door to evidence about Bradley’s shooting by repeatedly saying Hernandez couldn’t have killed Lloyd because they were friends.

The filing says Bradley was Hernandez’s “friend and confidante.” It says on the night of the shooting, Bradley, Hernandez and two other men went together to Tootsie’s Cabaret, a strip club in Miami. While there, Hernandez and Bradley got into an argument about how the bar tab would be divided, the filing said.

After they left the club, the filing said, Bradley realized he had left his cellphone there and Hernandez refused to go back. Bradley then made “disrespectful remarks” about Hernandez, prosecutors said.

“Shortly thereafter, the car pulled over in an isolated industrial area, where Bradley was shot between the eyes. The defendant exited the car and quickly dumped Bradley’s body on the ground before fleeing the scene,” prosecutors’ filing said.

Employees at a nearby store found Bradley minutes later. Bradley was seriously injured and lost an eye but survived. At the time, he refused to cooperate with police, telling them he didn’t know who shot him.

Hernandez, who grew up in Bristol, Connecticut, has not been charged in Bradley’s shooting, but Bradley sued him.

Prosecutors argued Monday that the shooting showed Hernandez just four months before Lloyd’s killing “shot another one of his friends in response to the most trivial provocation.”

Hernandez’s defense team previously argued against letting the jurors hear about the Florida shooting, saying if they were told about it they could jump to the conclusion Hernandez also shot Lloyd.

“This is precisely the kind of outlandish, flawed reasoning which our criminal justice system prohibits,” they wrote then.

The judge didn’t take up the prosecutors’ request Monday, and the defense hasn’t replied to the filing.

Hernandez also is charged in the 2012 killings of two men in Boston after someone spilled a drink on him at a nightclub. He has pleaded not guilty and will be tried later. The judge has ruled prosecutors in the Lloyd case cannot tell the jury about those slayings.

Bradley also has been mentioned in connection with that case. Police have said surveillance camera recordings show Hernandez and Bradley going into the nightclub shortly after the victims went in. They have said the recordings also show Hernandez driving an SUV out of a nearby parking garage with Bradley as a passenger shortly before the shootings.

Also Monday, Lloyd’s sister Shaquilla Thibou testified she saw him get into a silver Nissan outside their home around 2:30 a.m. shortly before he died. She said she could not see the driver.

Thibou also testified about text messages she exchanged with her brother soon after. The judge previously said prosecutors could not ask her about what the text messages said. In one, he told her he was with “NFL.”

Thibou testified that she received four text messages from Lloyd between 3:07 a.m. and 3:23 a.m. Prosecutors have said he was dead within minutes of sending his final message.