No, TurboTax doesn't file the IRS' Form 8379, Injured Spouse Allocation with your Colorado return.
You should file your Colorado injured spouse claim separately from your state return. According to Intercepted Refund Due to a Spouse's Debt on Colorado's Intercepted Refunds page:
If a refund is requested on a joint return, and the refund was intercepted due to taxes owed or a balance is owed to another Colorado government agency or the IRS, the spouse who does not owe the debt may request that he/she receive the portion of the refund that was intercepted.
Injured spouse claims should be mailed to the department separate from the Colorado income tax return. Claims must include a copy of the federal income tax return or federal form 8379 (available on the IRS Web site) and copies of all W-2, W-2G, or any 1099 statements received by both parties. Send all injured spouse claims to:
Colorado Department of Revenue
Injured Spouse Desk, Room 240
PO BOX 17087
Denver, CO 80217-0087
