1:39 PM PT -- Palm Beach Gardens Police chief Dominick Pape just told reporters the incident looks like it was "a random act of violence."

"It does not appear that Boucher had any legitimate purpose for being at the golf course," Pape said.

The law enforcement official added that Boucher -- who has a lengthy history of arrests -- was also reported missing by his family less than one hour before the golf course confrontation occurred.

A Florida golfer was arrested for murder at a course on Monday ... after authorities say a witness saw him savagely beat a man with several clubs -- and then drown the guy in a nearby water hazard.

The Palm Beach Gardens Police Department said in an incident report, obtained by TMZ Sports, the scene all played out at around 1:22 PM on the first hole of the Sandhill Crane Golf Club.

Officers wrote in the docs that a witness told them they saw 36-year-old Junior Boucher quarreling with 65-year-old Brian Hiltebritel ... when they heard Hiltebritel scream out, "He's trying to kill me."

It's alleged Boucher hit Hiltebritel several times with multiple clubs repeatedly ... until the two ended up in a pond.

"Once in the water," officers said a witness told them, "Boucher jumped on top of Hiltebritel and appeared to be choking him. Boucher then got off of Hiltebritel who was no longer moving and retrieved a golf club and struck him repeatedly in the head."

Cops stated the witness said Boucher then got out of the water, took off his clothes and started to walk away.

Police said when they arrived on scene, Boucher tried to evade officers -- but after they used an electronic control weapon, they were able to take him into custody.

As for Hiltebrital, cops wrote in the docs life-saving efforts were made ... but he was pronounced dead at the scene.

Boucher appeared in court Tuesday to face one charge of first-degree murder ... and at the proceedings, a judge denied his bond. Boucher is now slated to return to court next month.

It's not yet clear what Boucher's relationship with Hiltebritel is ... cops are expected to speak more on the matter later Tuesday.