10/24 2:49 PM PT -- Sam Underwood will not be charged for the arrest ... the Los Angeles City Attorney's Office has rejected the case.

A spokesperson for the City Attorney tells TMZ ... "After careful review, prosecution has been declined because there is a lack of sufficient evidence to prove the matter beyond a reasonable doubt."

Sam Underwood, famous for starring in "Fear the Walking Dead," ended up in LAPD custody after he allegedly roughed up a woman.

Law enforcement tells TMZ ... cops responded to a 911 call about a disturbance in a Los Angeles-area apartment around 2:30 AM on Oct. 7 and when police arrived, they were told Sam and a woman had gotten into a heated argument that got physical.

Cops tell us the woman had visible marks on her body and Sam was arrested for felony domestic battery. We're told the actor was hauled off to jail, where he was booked and released after spending close to 10 hours in custody.

It's unclear what his relationship is with the alleged victim. Sam's case, we're told, will now be submitted to the L.A. County District Attorney's Office for possible criminal charges.

As for the woman, cops say, although she had marks, she did NOT require medical attention.

A source familiar with the case tells TMZ ... Sam has provided his attorney with photographs, video recordings, and audio recordings -- all of which disprove the claims of the party making these accusations against him. We're told his attorney intends to provide this evidence to the police early this week.