State tax credit when filing part time resident

I am filing both CT and MA part time resident state taxes.  If I was taxed by CT for my last week of work in May, but was a resident of MA by then, can I claim the MA tax credit on that portion of my income? I have already finished my CT form. When I portioned/allocated out that last weeks pay income to MA shouldn't CT refund me anyways on that income, so I would not be taxed in both states, thereby not entitled to a MA credit?  If I can take the MA credit on the screen asking for "Income taxed by another state", are they asking for just the income I paid taxes on for that week, and not total income for the year? and second box asks "total tax liability before credits,W2 withholding and payments" is that the total tax liability I owed CT for everything on income on my 1040CT or just for that week?