Certified GKH Gardening Expert
It depends on the type. Some can only survive down to zone 7 and some can go to zone 4. If you aren't sure what type you have then it will be best to bring it in when the temperatures reach 10 degrees or so.
This article will help with the care of ligustrum: https://www.gardeningknowhow.com/.../ligustrum/growing-ligustrum-shrubs.htm