Legal Question in Intellectual Property in California

No, for registration purposes the criteria are the same for all types of ownership entities.

I don't think so; copyright however may be looking for authorship by an individual rather than an organization. I have yet to read a novel written by a corporation.

There are not different registration criteria for organizations (meaning whether an entity can own the copyright or trademark) but there are a number of other considerations to determine before filling out the applications, such as, is this a work made for hire, should you deem the owner of the association as the owner of the intellectual property and have him or her license it to the association for asset protection purposes, etc.

The answer to your question is not cut and dry.

No. But if you're copyrighting the name of the association, you need to be sure you fill out the form correctly. People often make mistakes in the authorship and ownership sections when they file for organizations. Read the instructions carefully and follow them.