You can sue anyone for anything at any time. It is more a question of who is going to pay, and how?
If you have been assaulted and injured at an apartment complex, you should contact a personal injury lawyer immediately. While the individual responsible for the attack is always liable, a personal injury attorney can investigate the facts surrounding the attack and determine if the apartment complex should face any liability as well.
Did they have adequate lighting? Was there security on duty patrolling? Should there have been? Is this a dangerous area? Is it a dangerous complex? Were there previous assaults? Was the criminal a tenant of the apartment complex? Were there warning to residents of previous assaults?
An experienced attorney in Austin can assess all avenues of liability and determine who bears responsibility.