Nathan Marlowe and his wife Cynthia Manzo said Simmons attacked them, threatened them and took their video camera at the upscale The Grove mall on Saturday after they started filming the rocker.
The couple's attorney, Matthew Nezhad, says a police report was filed. The couple sought a restraining order against Simmons on Wednesday, but that petition was denied.
Simmons has not been arrested and no charges have been filed.
According to the complaint and restraining order application, Marlowe asked Simmons for his view on monogamy, and Simmons responded by telling Marlowe to get his shot and leave. The filings state Simmons then lunged and attacked Marlowe, taking the video camera, then turned on Manzo when she tried to get the camera back.
A phone message seeking comment from Simmons' entertainment attorney was not immediately returned.
The couple are seeking damages of more than $25,000 for civil claims of assault, battery and infliction of emotional distress. The lawsuit was filed as a verified complaint, meaning Marlowe and Manzo signed it under penalty of perjury.