The City of Austin does have an ordinance about unrestrained dogs.
§ 3-4-1  UNRESTRAINED DOG PROHIBITED.

(A)   Except as provided in Section 3-4-4 (Public Areas Where Restraint of a Dog is Not Required), an owner or handler of a dog shall keep the dog under restraint.

(B)   A person holding a dog on a leash or lead shall keep the dog under control at all times.

(see http://www.austintexas.gov/department/animal-protection-ordinances)

• If the dog is loose, call 311
• If the dog is loose and is acting aggressive, call 311
• If the dog is loose and close to a school/area with children, call 311 (and definitely mention that)
• If the dog is loose and currently attacking another dog or person, call 911

Animal Control Services respond (come out) to loose dog calls Mon-Fri, 7 a.m.-4:30 p.m.; Sat/Sun 7 a.m.-6:30 p.m. and from 6:30 a.m. to 2 p.m. on city holidays.  If issues outside of these hours, call 311.

If you have had issues with an owner who habitually lets their dog out (aggressive dog or not), call 311 and report the issue and the owner’s address. Obviously, we want to talk to the neighbor first to solve but if no luck, then call 311.  The Animal Control Office will then investigate the situation and discuss with the neighbor. If the dog is out, owner can be cited and dog impounded where owner has to pay to get dog back.

For additional information on vicious and aggressive dogs, http://www.austintexas.gov/department/dangerous-and-vicious-dogs