In Colorado, you are generally not liable for injuries to your neighbors if they decide to trim branches from a tree that encroaches onto their property, provided that the trimming is done by them or their authorized agent. Without your neighbor actually being injured and the circumstances surrounding the injury, however, it is impossible for me to tell you what your legal liabilities are. Specific facts are applied to the law to determine liability.

The case of Savage v. Williams, 2018 Colo. Dist. LEXIS 1542 may be of interest to you. A plaintiff successfully demonstrated that the defendant's overhanging tree branches constituted a private nuisance, as falling ice from these branches caused a dent in the Plaintiff's truck. The Court ruled for the plaintiff and ordered the defendant to pay for the repair. The plaintiff was allowed to go onto the defendant's property to trim the trees.

Your situation also has parallels to encroachment trees, which "are those that begin life entirely on one person's property only to migrate partially to another's." Love v. Klosky, 2018 CO 20, ¶ 3, 413 P.3d 1267, 1268. Neighbors may remove encroachment trees without first securing the approval of their neighbor many circumstances.

Another potential area of liability arises if no action is taken regarding the tree branches, depending on the danger they pose. Your liability in this case would be determined based on whether you failed to exercise reasonable care to protect against dangers you knew or should have known about. Galef v. Univ. of Colo., 2022 COA 91.

You may be interested in this Q&A on neighbor tree disputes and this video on How to Manage Bad Neighbors.