The Texas State Library does lookups in vital records indices.This information is from their website:
Suggestions for research in the vital statistics indexes: The most successful research is that done in person. If you are unable to visit the Genealogy Collection, you may borrow microform copies of the indexes through the interlibrary loan program. Your public library will be able to assist you with this request.
A list of private researchers is also available upon request.
Although the staff does not undertake genealogical research or verification, we will check the indexes for names of specific individuals. Due to the high volume of requests, we must limit each request to 5 single names or years. Once we have responded to your request, you are welcome to submit another.
Requests may be submitted by e-mail to: firstname.lastname@example.org