New Mexico does allow a state tax credit of up to $2,800 for Long-Term care insurance premiums as part of your medical expenses if you are 65 years old or older.  This would only apply if your total medical expenses equal or exceed $28,000 during the tax year which were not reimbursed.  You also could be entitled to an exemption of $3,000 assuming you are over 65 years old.

I recommend reviewing your input in the state tax interview section.  

You can access your state income tax return by selecting State in the black panel on the left hand side of your screen when logged into TurboTax.

1. This will take you to a screen titled Let's get your state taxes done right.  Click continue on this screen.
2. You will see the following screen titled Status of your state returns.  
3. Select Edit to the right of your state return and go through the questions again.

As you go through the questions, you will be prompted to enter your medical expenses.  You will enter your medical expenses, including the amounts for your Long-Term Care insurance premiums in this field.

The next screen titled Medical Deduction will give you the amount of the deduction/credit you are entitled to assuming you meet all of the requirements.