If I purchased a second home in a different state than I work and live in, do I have to file a tax return in that state since the property taxes are paid in that state?

No.  Until you sell or utilize this second home in a business venture such as a rental property, there is nothing to report in MA.  You can deduct the amount paid for your real estate taxes and mortgage interest on both homes on your federal return if you itemize deductions. 

CA Itemized deductions:

CA does not allow a deduction of state and local income taxes on your state return.

CA does allow deductions for your real estate tax and vehicle license fees. I do not see any differentiation for property owned in another state.

Wonderful, thank you so much! Very helpful