Not just state and local laws, Federal law as well.
In most cases age, religion, marital status, disability, gender and race should be viewed as out of bounds. The exceptions where they are permissible are narrow (for example, a church can inquire about the religious beliefs of someone under consideration for a pastoral position but, in generally speaking, not a janitorial job).
In some states and localities the impermissible categories include sexual preference, criminal records, personal finances (i.e., credit scores, bankruptcies, etc.).
Check on the relevant law in the jurisdictions where you are hiring.