You pay taxes on your active duty earnings to your home of record state, not the state in which you are stationed. Assuming you meet all three prongs of the non-resident test for CT, you'll have to file a return to reclaim the improper withholding.
If you meet all three conditions for being treated as a nonresident for the taxable year but you had Connecticut income tax withheld from your military pay in error, you must file Form CT-1040NR/PY to request a refund. Complete Lines 1-5 following the directions on the form. Enter “0” on Line 6 if you had no income from Connecticut sources. Complete the rest of the form including the withholding information under section 3 of the return. Attach a statement to the front of the return stating:
* That you did not have a permanent place of abode in Connecticut during the taxable year;
* The location and a description of the permanent place of abode you maintained outside Connecticut and the beginning and ending dates of your stay there; and
* The exact number of days you were in Connecticut during the taxable year.
