Massachusetts income tax form instruction says this:

"How Do I Calculate My Rental Deduction If I Am Married Filing Separately?
If married taxpayers file separate returns, they are each entitled to a rental deduction equal to 50% of the rent each pays, not to exceed $1,500 per return. However, a married couple filing separately may allocate the rent deduction differently, provided the amount taken by each spouse does not exceed 50% of the rent actually paid by that spouse, and provided their combined rental deductions do not exceed $3,000. If this results in one spouse claiming a deduction in excess of $1,500, that spouse must enclose with his/her return a statement signed by the other spouse indicating consent to the allocation. The statement must contain the name, address and Social Security number of the consenting spouse and the amount of rental deduction taken by that spouse."

How does the above apply if taxpayer is filing MFS and the spouse stays in a different state? Can the taxpayer claim the full $3000 with a statement from spouse indicating $0 rental deduction? Or will it be limited to $1500?

You can claim the full $3,000 for your share of the rent allocation, but your spouse has to provide a written statement that she agrees and consents to you claiming the full $3,000 deduction.

Last year, I did file the MA MFS tax return claiming the full $3000 rental deduction and sent along a written consent statement from spouse. However, Massachusetts sent a correction in income tax return limiting the rental deduction to $1500.

So I guess if the spouse doesn't live in MA, the spouse cannot really give the consent to use the other $1500?

It looks that way.

"and the spouse stays in a different state". I believe it only applies to BOTH spouses living in MA. Hard to imagine they would give you basically 2 exemptions when one is , for example, living in California. Interesting "loophole"