One facility is the Jesse James Farm and Museum in Kearney, Kan., while the other is the Jesse James Museum in Wichita, Kan.
And the dispute centers around yet another DNA test to prove which body is that of the famed late outlaw.
The Kansas City Star says flap arises despite a 1995 exhumation in which testing established a 99.7 percent certainty the body buried in Kearney is that of James.
But challenger Ron Pastore of Wichita opened the Wichita museum and has had a Kansas man exhumed.
Pastore believes Jesse James faked his death and lived under the alias of Jeremiah James in Neodesha, Kan., where he was buried in 1935.
Pastore said he's awaiting DNA test results, which will be revealed on a History Channel TV special this fall.