Sen. John Whitmire of Houston received calls this month from death row inmate Richard Tabler, who used a smuggled cell phone.
Whitmire, who chairs the Senate Criminal Justice Committee, said the inmate described the lawmaker's daughters by name and where they live.
The phone was seized this week and Tabler's mother was arrested in Austin on charges she bought minutes for the device.
Whitmire, during the hearing in Austin, told prison officials he wants "zero tolerance" for contraband smuggling.
Gov. Rick Perry has ordered a system-wide prison lockdown and search.
Tabler was convicted of first degree murder and is awaiting execution in connection with the 2004 slayings of four people connected with a Killeen, Texas, strip club.
Previous Turner Report items about Tabler and his accomplice, 2004 East Newton High School graduate Timothy Doan Payne can be found at this link.