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    TEXAS (KTVT) -- The Texas Supreme Court has cleared the way for Robert Roberson's execution to be rescheduled a month after he narrowly avoided it. His attorney, Gretchen Sween, is hoping it won't be.

"This is entirely on the shoulders of the local district attorney in Anderson County," said Sween.

She is among those waiting to learn whether Allyson Mitchell, the district attorney in the county where Roberson was convicted of capital murder, plans to reschedule the execution.

"We would earnestly hope that she wouldn't, because during the recent legislative hearing she admitted that she had not read any of the new expert reports and to this date no court has read any of the new expert reports showing that Robert is innocent and how his daughter actually died," said Sween.

Prosecutors in 2002 argued Roberson's daughter had died from shaken baby syndrome using now outdated science. A judge halted his execution last month to allow him to testify before a legislative committee after several state lawmakers issued subpoenas hours before he was scheduled to die.

"His situation is one that can inform the way we write our laws, particularly the junk science law," said Rep. Joe Moody.

The lawmakers' actions raised questions addressed by the Texas Supreme Court Friday when it ruled, "the legislature's power to subpoena witnesses… is beyond question. But it is not absolute…"

"The committee's authority… does not include the power to override the scheduled legal process leading to an execution."

The Texas Department of Criminal Justice confirms it's up to Anderson County to arrange a new execution date. Mitchell has not responded to questions from CBS News Texas on when or if she plans to do so.

In the meantime, lawmakers say they still want to hear from Roberson.

"Maybe we need to travel there, but we intend to take Mr. Roberson's testimony," said Moody.

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