according to BicycleAustin.info:
"Proposed Statewide Helmet Law
In 2003, HB 2488 would have required cyclists under 15 statewide to wear helmets but the bill died in committee.
In Spring 1999, a similar bill applying to cyclists under 18 statewide to wear helmets came very close to passing (sailing through both a House and Senate committee with almost no opposition), but died at the last minute after a second senate committee didn't pass it. Below is some historical information about the 1999 bill."
http://bicycleaustin.info/laws/helmet-tx.htmlTexas does have a law that municipalities cannot pass such a law without instituting a bicycle safety education program in the schools:
"Statewide Helmet Laws (Texas)
As part of the Matthew Brown Act (HB2203), municipalities may not enact helmet laws for kids (16 & under) unless they have also instituted bike safety education in schools, and unless they have made provisions to provide helmets to children of low-income families."
http://bicycleaustin.info/laws/helmet-laws.html