It's a wise move to protect your posessions and yourself.
As a renter, you need insurance. While a property owner will most likely have insurance to cover the physical structure of an apartment building, that insurance does not cover the belongings of individual residents. Moreover, it doesn't provide you with liability protection.
Consider the value of your possessions and your ability to replace them if they are destroyed. If a disaster occurs, renter's insurance can help soften the financial blow.
More importantly, if a fire or other disaster occurs as a result of your negligence, you can be held liable for the cost of the repairs and can face the potential of litigation; without insurance you put yourself at unnecessary risk, but many renter's insurance policies can be written to help cover those liabilities should they arise.
Not only is renter insurance a good idea, sometimes it is a requirement for your lease. Many apartment properties include renter insurance as a lease requirement; renters who are accepted to lease an apartment must have proof of liability insurance when they sign the lease and when they renew.
Your agent who wrote your auto insurance policy can probably write a renter insurance policy. In addition to your your auto insurance provider, the Texas Department of Insurance can also prove to be a worthwhile resource. You can visit online at http://www.tdi.state.tx.us/or write:
Texas Department of Insurance
P.O. Box 149104
Austin, Texas 78714-9104