Police, called the next day, found Mills, 43, shot to death.
Arrested a week later in Layton, Boehme, 45, allegedly admitted to police that he fired a gun three times at Mills.
But when police asked him why he killed the man, Ogden police Detective Arthur Mackley testified that Boehme told them three different stories.
First, he said he thought Mills hit and raped his wife, Mackley testified Tuesday.
Then, he told police that Mills had threatened to overtake the storage shed business that Boehme had been running.
After that, Mackley said, Boehme told them that he felt threatened by Mills.
"He said [Mills] had positioned one of his feet in a stance indicating to him that he was going to be attacked," Mackley testified.
After hearing testimony from Mackley and other law enforcement officials, Judge W. Brent West ruled there was probable cause for Boehme to stand trial on charges.
Boehme then pleaded not guilty to three charges: first-degree felony murder and two counts of second-degree felony possession or use of a firearm by a restricted person charges.
He will appear in court again on Sept. 3 for a scheduling hearing.
Police went to the storage unit near 2900 Pennsylvania Avenue on May 29, after a woman called and said she had found a body in the one of the units.
Inside unit #79, Mills' body was covered by a blanket. He had been shot twice in the chest, and once in the head.
Utah Medical Examiner Joseph White testified Tuesday that the two chest wounds were very close to one another, and that gunpowder stippling showed the shooter was likely just feet away when Mills was shot in the head.
"Even in the best circumstances, any one of the three [wounds] would have caused death," White said.
Inside the storage unit, police found the revolver used to shot Mills and a sawed-off shotgun inside a backpack.
Boehme has a substantial criminal history, mostly drug-related convictions, according to a search of Utah court records. His most recent conviction was in 2009, where he pleaded guilty to driving on a revoked license and having a "speed contest" on a highway, and several drug-related charges were dismissed. He was ordered to complete drug court in that case, according to court records.
Court records indicate that Mills was released from the Davis County jail on April 11, after being convicted of violating a protective order, interfering with an arresting officer and failure to stop at the command of police.
Mills' other recent criminal history revolves primarily around multiple protection order violations over the last six years, according to court records.