Welcome to the forum. It sounds like you probably have either a loose or leaking connection on the back of the city water inlet. Possibly, since it hasn't been used since last season, the one way valve on the back of the inlet may have frozen and cracked over the winter.
Here are a few pictures of what your water inlet looks like. The configuration of water tank fill and city water hookup may differ, but the basic components, hose connector, one way valve, mounting flange and connection to the plumbing supply lines are pretty much the same in all trailers of your vintage.
You can purchase a new city water inlet and probably solve your problem. Cost should be about $8-10. Don't forget to buy a roll of BUTYL putty tape. You'll definitely find more uses for it in the next few weeks as you notice voids around windows, doors, access doors, molding, awning supports and the list goes on and on.
The last photo is a drawing of the basic water system for your trailer. It should help you understand how your water system works and help you understand the components.
Anyway, here are the photos of what you'll find when you pull the three screws that hold the city water inlet on the side of your trailer. Chances are you will find something leaking on that assembly.
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS