Yes.  

Massachusetts allows a deduction for moving expenses.  But as a part-year resident, your expenses may be prorated based upon your dates of residence.

You will still need to enter the moving expenses in the federal section of the program.

1. Select Deductions & Credits 
2. Select All tax breaks and scroll down until you see Other Deductions and Credits 
3. Select Moving Expenses 
4. Proceed to go through the screens and enter the information as applicable 

Great news..... Thank You!

Can we ask one more question here?  With the Turbo Tax software automatically prorate the amount or will we need to do that manually before entering the amounts?

According to this Turbo Tax reference, you will apply all moving expenses to the state you moved to, which would be Massachusetts. There are no allocations to be made.