Does the state of Colorado allow deductions for Long Term Care?

No, but it allows a credit.  A credit is generally better, since it offsets tax that you owe. A deduction merely lowers your income. 

To enter your long-term care information in TurboTax Online: 

1. Open TurboTax Online
2. Select Tax Home in the left pane
3. On the Hi, let's keep working on your taxes! screen, select the dropdown on the right side of the State Taxes box, then select Start, Continue, or Pick up where you left off
4. Proceed through the state screens until you come to the Take a look at Colorado credits and taxes screen
5. Select Start or Edit to the right of Long Term Care Insurance Credit
6. You should be on the Enter Your Long Term Care Insurance Credit screen. If you have more than one policy, enter an LTC amount and the number of people covered next to Policy 1, then do the same for Policy 2, and Policy 3, if applicable.

If you have more than one policy, but include all of your information in the Policy 1 fields, you'll only receive $150 in credit. 

See the Colorado Department of Revenue's Income 37: Long-Term Care Insurance Credit fact sheet for information about the credit.