The attorney for a Holtsville man shot in the shoulder by a Suffolk police officer in Medford earlier this week, is asking the state attorney general to oversee the Suffolk district attorney’s prosecution of his client for allegedly driving drunk and dragging the officer with his vehicle.

Authorities say Michael Shear, 34, was nearly three times the legal alcohol limit while driving when he dragged the police officer during a traffic stop that ended with the shooting. His defense attorney said the district attorney cannot fairly prosecute Shear while also investigating the merits of the officer’s actions.

An “investigation into the facts surrounding a police officer discharging his or her firearm must be examined by a truly independent agency,” said Steven Politi, of Central Islip, in a letter Thursday to Attorney General Eric T. Schneiderman.

While state law allows a court to appoint a special prosecutor in criminal cases when a conflict is determined, the prosecutor role is usually designated for a district attorney from another county within the same judicial district — not the attorney general.

Separately, a 2015 executive order from Gov. Andrew M. Cuomo gave the attorney general the authority to act as a special prosecutor, but only to investigate the deaths of unarmed civilians by law enforcement.

“The AG does not have jurisdiction to unilaterally take up this case,” Schneiderman spokeswoman Amy Spitalnick said in an email.

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Politi, in his letter, also accuses the Suffolk police and the district attorney’s office of “continuing to operate in their usual secretive and dishonest manner.”

A spokesman for District Attorney Thomas Spota, whose office investigates all police-involved shootings, did not respond to a request for comment.

A police department spokesman also did not respond.

Shear is being held at the Suffolk County jail in Riverhead on $75,000 cash bail and has pleaded not guilty to charges of felony DWI, first-degree aggravated unlicensed operation of a motor vehicle, second-degree reckless endangerment and third-degree fleeing an officer in a motor vehicle.

Police and prosecutors have not said whether Shear was armed during the incident, but he is not facing any weapons possession charges. His lawyer said he was unarmed.

According to prosecutors, Shear had a .22 blood alcohol content about an hour after the officer, whose name has not been released, shot him in the left shoulder. The highway patrol cop pulled Shear over at 2:38 a.m. Sunday in Patchogue for speeding and Shear took off, dragging the officer for several feet, prosecutors said. He injured his right arm, shoulder and hip.

Several officers then chased Shear’s vehicle and the same officer who was dragged, prosecutors allege, then shot Shear after he failed to follow commands.