Should I refinance if I plan on moving soon?
Most lenders charge fees to refinance a loan. So, if you plan to only stay in the property for a couple of years, your monthly savings may not accumulate to recoup these costs. Example: A lender charged $4,000 to refinance your loan that resulted in saving you $200 each month; it would take 20-months to recoup your initial costs.
If you take a no closing cost loan, then whatever monthly savings you will get is all to the good. It's costing you nothing to refinance, so go ahead and do it.