It's a rental, so I don't see much benefit to refinancing because of the investment property premium. You would finance a lower amount at the same or slightly lower interest rate. You are not likely to save enough to make it worth the cost. The property is now 10 years old, so the maintenance is going to increase. The appliances and hot water heater will likely have to be replaced and there may be furnace/AC issues in the next few years. The roof probably has 5 to 10 years, depending on your climate. When you add in vacancy and collection loss plus repairs and maintenance, you will be out of pocket over time. You will experience a vacancy at some point and you will have turnover costs when that happens.
Unless you see rents and/or values going up over the next few years, or you believe there is a good possibility you would occupy the property again, I would consider selling. You have a loss that is larger than the depreciation recapture at this point so taxes should not be an issue. If Zillow is right, and it rarely is, you would probably have to bring a little cash to the table to sell. But it's not going to generate any cash flow for a long time and it has the potential to cost you thousands if a major capital improvement is required.
In your shoes, I would talk to a knowledgeable local real estate agent or two to get a better picture of market value and I would get the refi details from a couple of lenders. With that information, you will be able to make a more reasoned decision.
