It really does depend on what your current rate is and what rate you will lock into by refinancing. You should talk to a mortgage professional that you trust or someone at your bank to determine what your monthly savings would be.
Any bank would have an appraisal done to make sure that the property is worth at least what the loan amount is. If you are really upside down re-financing may not be an option, AGAIN I AM NOT A MORTGAGE PROFESSIONAL. Check with one before you do anything.!!