You usually will need  a permit to remove or severely prune a tree within the public right-of-way, such as the area between the sidewalk and the curb.  See Newberg Code 12.05.260.

You usually also need a permit to remove a tree within a stream corridor. See Newberg Code 15.342.110.   You can view the Newberg interactive map at the link below to determine if the tree is within a stream corridor.

You need permission to remove a tree that was required as part of a design review approval.  These are usually trees in commercial or multi-family developments,  such as a landcaping tree in the front yard or within a parking lot.  If the tree was required to be preserved as a condition of approval for a development, then it is subject to the conditions of that approval.

Otherwise, the City does not require a permit to remove or trim trees on private property.  You must have permission of the land owner.  If you need to block the right-of-way to remove the tree, you will need a permit for that.

The property owner must remove hazardous trees, and keep trees trimmed above sidewalks and streets.  See Newberg Code 8.15.100.

You may need permits from the Oregon Department of Forestry for logging operations.  Go to
http://www.oregon.gov/ODF/privateforests/fpaKeys.shtml

If you have questions, talk with the Planning Division at 503-537-1240.