Non-Resident Tax Returns?

[ish1521]

I am having a problem with my CT tax Return. In Ct I made 5942 in wages and pd 286 state income tax.

On the program Im using IT states that I claim the alternativve Minimum Tax which make me OWE 1789 dollars which doesn't make much sense to me because that would mean I'm paying 2075 dollars in taxes to just CT, which is more than I paid into my resident state and any of the other 4 non resident states.

SO what im asking is Do I have to pay the amt on my non resident returns? or do I have to?