Legal Question in Real Estate Law in California

You'll find precious little in the statutes. The law is primarily non-statutory, judge-made, case law.

An action for harm done by a tree on adjoining property could be brought either as one for trespass, or for private nuisance, or both.

For a definition of "private nuisance," see Civil Code sections 3479 - 3481. Remedies for private nuisances are discussed (briefly) in CC sections 3501 - 3503. Ownership of trees is covered by CC sections 833 and 834. There are sections dealing with trespass TO trees, but the issue here is trespass BY trees.

Turning from statutes to case law, we find numerous cases detailing the relative rights of tree owners and neighbors affected by invasive roots, overhanging limbs, blowing leaves, and so on.

Without knowing the mechanism by which the cottonwood is causing damage, I'm somewhat inhibited in giving you case law references or guessing whether a suit for trespass or for private nuisance might be successful. If roots and/or limbs are invading your property, you'd probably have the right to cut them at the property line. If it's just blowing leaves, you may have a tougher time; courts are less willing to require a tree be cut down just because its falling leaves make a mess on the neighbor's yard.

I am somewhat inclined to think you may be right and the HOA wrong here, but more facts would be necessary in order to look at decided cases and figure how a court might rule on this. The answer almost certainly isn't in the codes, however.