Police said Tuesday they have a "near confession" from a National Guard sharpshooter being hunted in the Wyoming wilderness in the sniper murder of his singer wife.

Cheyenne Police Capt. Jeff Schulz said investigators had discovered a note that led them to file first-degree murder charges against Davis Munis, 36. Schulz said it appeared Munis had "left the note" for investigators to find.

Police confirm that in the note, which spans five or six pages, Munis wrote reasons for wanting to kill his estranged wife, Robin. Schulz would not elaborate any more on the substance of the note.

Authorities say Munis stalked Robin Saturday night as she performed with a country band at a restaurant outside Cheyenne. Munis killed her with a single shot while she sang on stage at Old Chicago restaurant, investigators charge.

Earlier Tuesday, officials found Munis' black Dodge pickup truck in Roger's Canyon near Laramie after a tip from a caller. That caller also claimed to have spotted Munis in Laramie, about 45 miles west of where his wife was shot dead.

"He is our sole suspect right now," Schulz told FOX News. “It’s gonna be a slow, methodical, tactical search.”

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Meanwhile, a National Guard helicopter continues to fly over a 10-square mile area north of Laramie while six teams of four scour the land on food.

So far, officials have found no trace of Munis, and have not ruled out the possibility he had a vehicle waiting for him when he left the truck.

Schulz said police had not yet searched the vehicle, which had National Guard license plates, but sources told FOX News that investigators had found an empty handgun case and that two canteens were missing from the truck.

"We’re presuming he’s got handguns, at least one,” Schulz said, referring to the firearm missing from the truck. "He’s in a wooded canyon, a very remote area."

A Blackhawk helicopter was aiding the ground search for Munis, who was believed to be on foot.

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Lead singer Ty Warner was standing next to Robin as a bullet shattered the eatery's glass door and struck her in the head as she sang Toby Keith's "I Love This Bar" on stage Saturday.

“I heard a pop … and there was a puff of smoke," said the Ty and the Twisters bandmate, adding that he thought a spilled drink on the electrical equipment had caused the smoke before realizing Robin Munis had been shot.

Warner said Munis, 40, who recently had moved out of her home with her four children during the estrangement process, continued to balance her responsibilities to her family and job as a policy analyst and to the band.

"She was a consummate professional," he said.

Police said that after searching his home, they assumed David Munis had at least one high-powered rifle with him. Schulz has said the search also turned up evidence connecting Munis to the shooting, though he did not elaborate.

He did say, however, that Munis had not touched his bank account or used his cell phone since the shooting.

Munis has been a member of the Wyoming Army National Guard since 2003, previously in the U.S. Army and was a 2001 graduate of the Army Sniper School at Ft. Benning, Ga., according to the National Guard.

"Apprehending a man with that kind of sniper skill and the weaponry he has available to him is an extremely dangerous type of proposition," Schulz said Monday.

Schulz said investigators were speaking to David Munis' relatives in Montana and a friend at an Army base in Kentucky with whom he had been in contact. Authorities didn't specify which base, but the Munises had lived within a few miles of Fort Campbell, Ky.

Neighbors Laura and Eddie Lopez said they didn't see any violence between the Munises, who they said were a very friendly couple.

Between them, the Munises had four children, ages 19, 17, 13 and 5.

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The Associated Press contributed to this report.