The Texas Supreme Court on Friday said the execution of a man convicted of murder in the 2002 death of his 2-year-old daughter could move forward, even as a state house committee seeks to subpoena the man for his testimony and its bipartisan members fight to spare his life.

Roberson was convicted of killing his 2-year-old daughter in a “shaken baby” case that many say led to an innocent man’s death sentence.

The Texas Supreme Court on Friday ruled a House committee overstepped its authority when it effectively stalled Robert Roberson’s execution by issuing an eleventh-hour subpoena. The ruling clears the way for prosecutors to seek a new execution date for Roberson.