Cook Children's Medical Center has filed an emergency motion, asking the state Supreme Court to expedite the review of the Tinslee Lewis case.
The Fort Worth hospital said the little girl's suffering has only increased since a temporary injunction hearing last December.
A judge ruled the hospital could not remove Tinslee from life-sustaining treatment.
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Doctors say Tinslee won't ever improve and is in pain.
Her mother doesn't believe she's suffering, and that any end-of-life decision should be hers to make.
Tinslee's mother Trinity sent NBC 5 the following statement.
"Cook's recent court filings are wrong. I visit Tinslee every single chance I get. I have fought with Cook Children's on which members of my family can visit Tinslee because they have very strict and limited visitation rules. Cook's will not allow me to visit Tinslee while bringing my baby daughter. As a single mother working two jobs, I have to find a babysitter so I can see Tinslee. I am fighting for her. Cook's recent court filings don't tell the truth about my little girl’s condition and show Cook's will say anything to have my daughter’s life ended."