No. An unlawful detainer is a summary proceeding. As such, an unlawful detainer proceeding is given legal precedence over all other civil actions so that it can be quickly heard and determined. (Code of Civil Procedure §1179a.)
A cross-complaint is not permitted in an unlawful detainer lawsuit. A defendant has no right to file a cross-complaint or counterclaim because possession is the only issue being litigated in an unlawful detainer action. (Vella v. Hudgins (1977) 20 Cal.3d 251, 255.)
You must file a civil lawsuit for damages. The civil lawsuit may be filed as a small claims action, or a limited jurisdiction superior court action, or an unlimited jurisdiction superior court action.
Frank W. Chen is licensed to practice law in the State of California. The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, consult your own attorney.