If the tree is in the planting strip or right-of-way, you do need a permit from the City of Tacoma to trim the tree. The permit is free and can be done through the Permit Center.
Some private properties are located in "critical areas". If your tree is located in a critical area, you will need to get a permit.
Visit the pruning and removal pages for additional information on pruning in Tacoma.
If the tree is in your yard and it is not in a "critical area", you do not need a permit. We do suggest that you follow industry standards for pruning. More information about pruning can be found on the Pacific Northwest ISA Pruning Guidance web page.