I'm not an attorney. That may be a rather complicated question. Generally the fourth amendment applies, but if you are operating your RV as a vehicle on the roads then vehicular precedent may be important. I presume there may also be different laws depending on the state where you are residing in your RV.
https://www.uscourts.gov/about-feder...er%20the%20law.
"Whether a particular type of search is considered reasonable in the eyes of the law, is determined by balancing two important interests. On one side of the scale is the intrusion on an individual's Fourth Amendment rights. On the other side of the scale are legitimate government interests, such as public safety.
The extent to which an individual is protected by the Fourth Amendment depends, in part, on the location of the search or seizure. Minnesota v. Carter, 525 U.S. 83 (1998).
Home
Searches and seizures inside a home without a warrant are presumptively unreasonable.
Payton v. New York, 445 U.S. 573 (1980).
However, there are some exceptions. A warrantless search may be lawful:
If an officer is given consent to search; Davis v. United States, 328 U.S. 582 (1946)
If the search is incident to a lawful arrest; United States v. Robinson, 414 U.S. 218 (1973)
If there is probable cause to search and exigent circumstances; Payton v. New York, 445 U.S. 573 (1980)
If the items are in plain view; Maryland v. Macon, 472 U.S. 463 (1985).
A Person
When an officer observes unusual conduct which leads him reasonably to conclude that criminal activity may be afoot, the officer may briefly stop the suspicious person and make reasonable inquiries aimed at confirming or dispelling the officer's suspicions.
Terry v. Ohio, 392 U.S. 1 (1968)
Minnesota v. Dickerson, 508 U.S. 366 (1993)
Schools
School officials need not obtain a warrant before searching a student who is under their authority; rather, a search of a student need only be reasonable under all the circumstances.
New Jersey v. TLO, 469 U.S. 325 (1985)
Cars
Where there is probable cause to believe that a vehicle contains evidence of a criminal activity, an officer may lawfully search any area of the vehicle in which the evidence might be found.
Arizona v. Gant, 129 S. Ct. 1710 (2009),
An officer may conduct a traffic stop if he has reasonable suspicion that a traffic violation has occurred or that criminal activity is afoot.
Berekmer v. McCarty, 468 U.S. 420 (1984),
United States v. Arvizu, 534 U.S. 266 (2002).
An officer may conduct a pat-down of the driver and passengers during a lawful traffic stop; the police need not believe that any occupant of the vehicle is involved in a criminal activity.
Arizona v. Johnson, 555 U.S. 323 (2009).
The use of a narcotics detection dog to walk around the exterior of a car subject to a valid traffic stop does not require reasonable, explainable suspicion.
Illinois v. Cabales, 543 U.S. 405 (2005)."
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