Hi Sarah -
Since you don't owe anything on the unit, you're not looking to refinance a loan but to obtain a secured loan based on the value of the property. Most lenders should be able to do this, if you meet income and credit requirements, and the property appraises for an adequate amount. Since you own the property the unit is located on, it should qualify as real estate as long as it is permanently attached to a foundation and was built after June 15, 1976.
A mortgage generally refers to a loan secured by a property you intend to live in, so you're talking about a loan secured by an investment property. But you can get a secured loan backed by pretty much anything of value. Most full-service lenders should be able to help you with this.