There is no "CARFAX" service for travel trailers.
Please note CARFAX often misses a lot of the past history on vehicles.
They only report on issues reported to them by "reporting members".
If repairs were done by a non-reporting garage there would be no record.
Travel trailers are simple...what you see is what you get.
If you are new to this marketplace get someone to help you.
It would be great if someone in Kansas would chime in and offer local assistance.
All the checklists in the world will be of no value if you don't know what you are inspecting...experience counts.
The VIN (serial) number on the title must match the number on the trailer.
The title will either be free and clear or have an indication of a lien.
If there was a lien current owner must have lien cleared before sale.
It all works out to "Buyer Beware".
Get someone with knowledge to help you inspect the trailer.
Ask the current trailer owner a lot of questions. You will quickly get a sense of weather or not this owner took pride in ownership and maintenance.
Most important check the tires
...check production date...tires over 5 years old should be replaced. Once the trailer is yours keep the tires
covered when not in use. UV degradation from the sun and not mileage is the real enemy of trailer tires
Good Luck and Happy Camping!