Artem Chigvintsev's domestic violence arrest is moving along ... 'cause the Napa County Sheriff just turned the case over to the D.A. -- and, formal charges could be coming.

Napa County D.A. Spokesperson Carlos Villatoro tells TMZ ... their office is currently reviewing the case, and no decision has been made yet on charges the pro dancer may face.

We're told the D.A. will make a decision after a thorough review of the case and will then make a public announcement.

Villatoro says the D.A.'s office still needs to review witness statements, footage from the incident, photos that may have been taken or anything else the police found during their investigation.

Chigvintsev's arraignment is currently scheduled for November 4.

It's been a wild week for Artem, who was arrested last Thursday for corporal injury to a spouse or cohabitant after allegedly attacking wife Nikki Bella -- resulting in a visible injury that triggered his arrest.

The radio dispatch call obtained by TMZ confirms Artem called for medical assistance ... before calling back and asking paramedics not to come. Cops responded and arrested him at the scene.

Nikki's ditched her wedding ring in the aftermath of his arrest -- going ringless on Netflix's Joey Chestnut vs. Kobayashi hotdog-eating contest Monday -- and sources tell us she's looking for a divorce lawyer to end her two-year-long union to Artem.

The pair share one child -- 4-year-old son Matteo -- who is staying with Nikki in their family home, we're told. Artem is crashing with a friend.