Tyler Robinson — the 22-year-old suspected of killing Charlie Kirk — is currently being evaluated by jailhouse staff in a Special Housing Unit … TMZ has learned.

Utah County Sheriff’s Spokesperson Sergeant Raymond Ormond tells TMZ … tells us Tyler’s in the SHU under “Special Watch” while they work to determine if he’s a danger to himself or others — with mental health pros evaluating whether or not he’s suicidal.

We don’t know if he’s made any comments which could indicate he’s considering suicide in jail … though law enforcement sources told us earlier Friday that Tyler allegedly indicated to his father he’d rather die by suicide than turn himself in to police.

As you know … Robinson was arrested Friday and booked on charges of aggravated murder, felony discharge of a weapon causing serious bodily injury and obstruction of justice. He has not yet been formally charged.

Police claim he’s the person who shot Kirk in the neck at Utah Valley University Wednesday afternoon. Kirk was rushed to the hospital but died from his injuries.

Videos emerged which showed the alleged shooter — dressed in a black t-shirt, a cap and sunglasses — and police asked the public for help identifying the shooter before Robinson’s arrest. The probable cause affidavit states Robinson previously mentioned his dislike for Kirk to his family.

Charlie is survived by his wife Erika — who spoke on Friday for the first time since he was killed — and their two children. He was 31.