Jelly Roll is facing some heavy accusations from comedian Nicole Arbour … but police in Nashville say they’re not exactly rushing to build a case.

A rep for the Metropolitan Nashville Police Department tells TMZ, “As you’re probably aware, there appears to be an ongoing online back and forth between the two. No charges have been filed and there is no current investigation underway on the part of MNPD.”

That statement comes after Arbour publicly escalated her feud with the Grammy-winning singer … recently accusing his team of sending her an alleged “hush money” deal and threatening to sue her if she didn’t sign it.

Nicole has been blasting Jelly on social media … claiming she rejected the alleged agreement and calling him out for refusing to apologize for what she says has been years of behind-the-scenes threats involving him and his wife, Bunnie XO.

Now, things appear to have gone beyond social media posts … according to an incident report filed March 1, Nicole told deputies she’d been dealing with “ongoing issues” involving Jelly Roll — listed under his legal name, Jason DeFord — and people associated with him.

Nicole told authorities she provided video she says captured the incident … and deputies say they reviewed the footage and identified Jelly Roll and another man in the clip.

Per the report, Jelly Roll allegedly referenced seeing Nicole at a charity event with a camera … and Nicole claims that’s when he allegedly said if he saw her with the camera, “he would kill her.”

The report notes deputies said they heard the alleged comment while reviewing the footage.