Massachusetts does offer a credit for education expenses. The credit is lessened by expenses paid through financial aid. The credit is also dependent on the taxpayer's income.
It is possible that the reason your refund went down is that the software had calculated the credit before the expenses were reduced by the financial aid.
As far as I remember, my MA refund did not go up after entering the school information in the federal return. Could there be any other reason, like going to an out of state school? I know I do not qualify for any MA refund for school because it was not a certain percentage of my income. The link posted does not work as well.
The credit relates to your income, not the location of the college.
Mass has a lot of unsupported items in the software right now. As the state updates forms, they are incorporated into the system. Please check Forms Availability for your method of tax preparation.