An earlier subpoena ended up delaying Roberson's Oct. 17 execution, which had been set to be the first in the U.S. tied to a diagnosis of shaken baby syndrome.
The House Committee on Criminal Jurisprudence announced it had issued last week and served on Monday a subpoena compelling Roberson to appear before it at a meeting in Austin on Friday.
The committee has argued it needs to hear from Roberson about whether a 2013 law created to allow prisoners to challenge their convictions based on new scientific evidence was ignored in his case.
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"Robert's testimony will shed important light on some of the problems with our 'junk science writ' process, a legal procedure Texas lawmakers expected to provide reconsideration in cases like this one," committee chair and state Rep. Joe Moody, a Democrat, and committee member and state Rep. Jeff Leach, a Republican, said in a statement.
The committee said it's waiting for a response from the Texas Department of Criminal Justice.
Amanda Hernandez, a department spokesperson, said in an email that her agency "doesn't have a comment at this time."
Roberson's lawyer said he's "grateful for the chance to be heard."
"I profoundly hope that his ability to appear is not obstructed by those who, for whatever reason, do not want the lawmakers and the public to hear from him directly about his experience trying to communicate his innocence," attorney Gretchen Sween said in a statement.
Roberson had been set to appear before the committee on Oct. 21 under the first subpoena. However, the Texas attorney general's office said he would only appear by videoconference because bringing him to the state Capitol would present "myriad security and logistical concerns."
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The committee and Roberson's lawyers have pushed for him to appear in person, saying testimony via video conference would be difficult for him because he has been diagnosed with autism and has communication challenges.
Roberson, 58, is being held in the Polunsky Unit in Livingston, located more than 200 miles northeast of Austin.
Roberson was sentenced to death in 2003 for killing his 2-year-old daughter, Nikki Curtis. Prosecutors said Roberson shook her violently back and forth. Roberson's attorneys have argued that the child's symptoms did not align with child abuse and that she likely died from complications from severe pneumonia.
Roberson has gained bipartisan support from lawmakers and medical experts who say he was convicted on faulty evidence of "shaken baby syndrome," which refers to a serious brain injury caused when a child's head is hurt through shaking or some other violent impact, like being slammed against a wall or thrown on the floor.
After the state parole board, multiple lower courts, and the U.S. Supreme Court had all rejected Roberson's request to delay his October execution, it appeared he would receive a lethal injection.
But the House committee used an unconventional strategy to delay his execution: issuing a subpoena for Roberson to testify days after he was scheduled to die. After legal debate in multiple courts, the Texas Supreme Court upheld an order to stay Roberson's execution.
In November, the Texas Supreme Court ruled that a legislative subpoena cannot stop an execution. But the court did say the committee could issue another subpoena for Roberson's testimony so long as it didn't block a scheduled execution. A new execution date for Roberson has not been set.
If the state criminal justice department would not comply with a new subpoena, the House committee could seek "judicial relief" to compel Roberson's testimony, the Texas Supreme Court said in its order.
The Texas Department of Criminal Justice and the attorney general's office had objected to the first subpoena because it would have forced the state prison system to disobey a valid court order to carry out a lawfully imposed death sentence.
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