It looks likely – the city is considering its own civil unions ordinance. KPHO reports:
Tucson is moving toward providing civil-union certificates to couples who cannot marry and allowing them to record contracts defining their relationships. Under a unanimous City Council decision Wednesday night, an ordinance will be prepared for a council vote this summer.
For those not familiar with Arizona politics, the Tucson area is generally much more liberal than Phoenix, its northern counterpart (although the actual city of Phoenix has become progressively more liberal).