Union police said Shults admitted he watched Marsch and "deliberated" killing her before walking from the park parking lot, approaching her from behind and strangling her.
"He said he was mad. He was angry in general about his life," said Union Police Chief Norman Brune. "He walked up behind her and killed her -ðit is very sad."
Shults, whose most recent address is in Washington, admitted to Union police to killing Marsch Friday morning near a picnic table at the park and dumping her body on private property off Judith Spring Road.
Brune said Shults was questioned Sunday in the abduction of Marsch after he allegedly kidnapped his estranged wife in Washington Saturday and later released her.
"During questioning he admitted to it and said 'I'll take you there,'" said Brune. "We couldn't believe how quick he said it."
Shults took officers to Marsch's body at 6 p.m. Sunday.
Brune said Shults was angry after disputes and legal troubles that were the result of the relationship with his estranged wife.
"In his words, she (Marsch) was in the wrong place at the wrong time," Brune told The Missourian. "He was angry at his wife."
According to the probable cause statement filed in Franklin county Associate Circuit Court by Union Lt. Kyle Kitcher, Shults saw Marsch sitting at the park and deliberated killing her, set down his shaving kit, walked behind Marsch and strangled her. He then loaded Marsch's body into the bed of his pickup truck and dumped the body.
Police said they don't know that Shults ever met or talked with Marsch before the murder.
"It's hard to understand how anybody can do something this violent to someone they never met before. . .," said Brune. "It's beyond comprehension, but it does exist.
"There is nothing that he can be mad about that could substantiate him killing a person who has nothing to do with his life - it doesn't matter," Brune added. "It's like a person who gets mad and punches a wall. It doesn't make sense."
Authorities said Shults is expected to be arraigned this week or next week and prosecutors plan to present the case to the grand jury in August.
Brune noted that police began questioning Shults Sunday about Marsch after the alleged abduction of his wife in Washington Saturday.
"That's what really alerted usð- too many coincidences," said Brune. "We had this incident here and she (Shults' wife) was taken against her will over there. We were very interested."
Police said Shults was "spending a lot of time at the park" and sometimes sleeping in his truck.
"He was flip-flopping between people he knows and sleeping in his truck," said Brune.
Shults was a 1982 graduate of Union High School and has children with his first wife who lives in Union.