Smoke detectors are required in all apartments and other rental units according to the Texas Property Code.  The Austin Tenant’s Council lays out the laws in Texas for how many detectors are required and remedies for getting them installed, repaired or replaced.
Landlords are required to install at least one smoke detector outside of every bedroom.  If the bedrooms are all on the same hallway, they can elect to put just one smoke detector in the hallway so it is still in the immediate area of the bedrooms.  If one or more bedrooms are on a level above the living and cooking area, the smoke detector for those bedrooms has to be put in the center of the ceiling right above the top of the stairwell.  Efficiency units are required to have a single smoke detector.
If smoke detectors are not in place when a tenant moves in, they can ask the landlord for them, preferably in writing whether the lease stipulates the request must be written or not.  The landlord is also required to inspect and test all the smoke detectors when the tenant moves in and after that when the tenant asks for an inspection or reports a malfunction.  This is also best to put in writing, even if the lease doesn’t say it has to be.  However, if the smoke detector is damaged by the tenant or his guests, the landlord doesn’t have to repair or replace the unit unless the tenant gives them the money for the repair or replacement before it is done.
If the landlord won’t put in a smoke detector, or inspect or repair one, within a week of getting a written request, the tenant can take the landlord to court and/or terminate the lease and move out.  
If a tenant doesn’t replace the battery in a smoke detector, or intentionally disconnects or damages a smoke detector, they can be held responsible for any damages that result from the non-working smoke detector.  
Other stipulations of the law include:  the tenant must be current on rent before requesting installation, testing or repair of a smoke detector; if either party files suit in court just to “harass the other party”, they can be fined a civil penalty of one month’s rent plus $100, plus lawyer’s fees and court costs; the tenant is unable to give up the right to a smoke detector, even in the lease; it is the tenant’s job to replace batteries if the smoke detector was working when they moved in; and finally, if required by a hearing-impaired resident, the tenant can request a smoke detector that is capable of alerting a hearing-impaired person in the bedrooms it serves.