Zachery Ty Bryan allegedly punched a woman multiple times and threatened to kill her before his arrest on January 1 ... TMZ has learned.

As you know, the former "Home Improvement" star rang in the New Year by adding another arrest to his rap sheet ... and, according to the incident report, officers responded to a call just before 7 PM on the 1st in Myrtle Beach, South Carolina.

Cops say they spoke to the alleged victim when they arrived at the scene ... and, she told them Bryan punched her multiple times on the left side of her face.

She also claims Bryan put his arm around her neck and choked her ... cutting off her breathing and making her fear for her life, she says.

During this alleged incident, the unnamed woman told cops Bryan said he was going to kill her. In the report, police say the woman had injuries consistent with her story.

In the report, cops wrote that the woman shares a child with Bryan ... though her name is not listed.

As we told you, Bryan was arrested for second-degree domestic violence ... and, in his mug shot, he sported what looked like several cuts to the left side of his face.

Bryan was initially being held on $10K bond ... but, online records indicate he was released around 8 PM Friday night.

This is far from Bryan's first arrest ... he was previously arrested for domestic violence in July 2023 and for DUI in February 2024.