Montana Department of Justice officials identified the 3-year-old boy as Broderick Daniel Cramer, of Lacey, Wash. His father, Jeremy Brent Cramer, has been charged with deliberate homicide and is in jail on $250,000 bond.
No other details were released about how the boy died, and authorities said an additional pathology examination and investigation is needed.
"It does appear that there was some sort of weapon used that caused the blunt-force trauma and also the sharp-force trauma," said Anaconda-Deer Lodge County Attorney Ben Krakowka.
Authorities have found what may be the weapon, but Krakowka declined to say what it was or where it was found.
Broderick's body was found Tuesday 5 miles southeast of Anaconda, Mont.
Authorities began searching for him after his father was arrested Monday night in a convenience store bathroom washing blood from his clothes.
They found the 38-year-old Cramer's truck on a rural road, and discovered the boy's body the next morning about 150 to 200 yards away, Krakowka said.
Cramer's wife told police her husband had left their home with their son Monday. Lacey Police Cmdr. Jim Mack said an Amber Alert wasn't issued because the mother never indicated that the child was in danger.
But police requested help from law enforcement in eastern Washington, Idaho and Montana in a search for the boy after the 31-year-old woman reported her husband's fuel card was used in Moses Lake, Wash.
Police say the couple had been arguing about finances.
"He had asked her earlier within the last couple of weeks if they could do a road trip to the East Coast, and she said, 'No, we don't have the money,'" Mack said.
Cramer had been living in Lacey for about a year and had a Montana's driver's license, Mack said.
Krawkoka said he had no information on Cramer's background.
Cramer has requested a public defender, but Krakowka said he did not know whether one had been appointed. Cramer made an initial court appearance Tuesday to hear the charges against him, and a new court date has not been set.
Police were still investigating the crime scene and interviewing witnesses on Wednesday.
The state Division of Criminal Investigation and the Anaconda-Deer Lodge County Department of Law Enforcement are leading the investigation.
AP writer Rachel La Corte contributed to this story from Olympia, Wash.