If it is in violation of governing documents of your association. It has to be recorded and published that vehicles without current registration may be towed. Although most associations allow for one warning sticker be placed on the vehicle if you ignore it they need not tell you.

if it's in their bylaws they can. especially if you signed saying you read and understood the bylaws.

They can tow your vehicle if it is in the Rules and Regulations. The Rules and Regulations would constitute your notice and they wouldn't need to give any further notice.

People seem to not realize that the Association owns the parking spots in condos and that they are part of the common areas.

Section 1. Title 33, chapter 16, article 1, Arizona Revised Statutes, is amended by adding section 33-1815, to read: Enforcing Association Parking Rules. The Association can enforce parking restrictions in its parking areas, as well as on its private streets. The Association may also enact and enforce rules that control parking on private lots (e.g., restrictions on parking in yards). If your Board wants to be able to tow non-compliant vehicles, proper signage is a prerequisite. Generally, the Association is deemed to have given consent to unrestricted parking by the general public on common area streets, unless signs are posted that are clearly visible and readable from any point on the streets, and at each entrance to the community. These signs must contain, at least, the following information: 1. Restrictions on parking (Number of hours, times of the day, etc.). 2. Disposition of vehicles found in violation of the parking restrictions (Where the vehicles will be towed). 3. The maximum cost to the parking violator, including storage fees and any other charges that could result from the disposition of the vehicle. 4. The telephone number and address where the violator can locate his/her vehicle after it has been towed. Be aware that a towing company cannot tow a vehicle from private property without the permission of the owner of the vehicle, unless the towing company either receives a request from a law enforcement agency, the express written authorization of the property owner (or the owner’s agent), or a court order granting the Association the authority to go onto the property and remove the vehicle. The Association typically is the property owner of the common areas and can authorize towing from those areas.