Private residence to rental & the Mortgage

[Account Closed]

I'm having trouble understanding how the follow works, or is done. 

You buy a property with a personal mortgage, and you are there for a couple years. And then you want to keep the property as a rental, and move into another place. Can you keep the same mortgage on the first place, or do you need to refi with a new mortgage because you don't live there anymore and it's an income property?