Nick Reiner‘s attorney Alan Jackson is getting a close look at the crime scene where Nick’s parents — Rob and Michele — were stabbed to death … he’s just been spotted visiting the home where the couple’s bodies were found by their daughter Sunday.

Jackson was fresh from the courthouse, where Nick WASN’T seen today, because he didn’t have medical clearance to appear in court.

Watch the video … you can see Jackson march down the usually quiet road flanked by news crews, causing a commotion with his arrival. Jackson carries a file with him, which he uses to gesture to his team, possibly instructing them on their first moves.

As you know … Alan is one of the most well-known criminal defense attorneys out there, and he’s no stranger to high-profile cases like this one … he recently got Karen Read acquitted of murder in Massachusetts.

In a press conference Tuesday, Los Angeles County District Attorney Nathan J. Hochman came out swinging, saying the death penalty is on the table if Nick is convicted of murdering his parents.

As we reported … Nick was arrested on suspicion of killing his parents after they were found stabbed to death in their Brentwood, California home Sunday afternoon.

TMZ broke the story … Nick got into a heated argument with Rob at Conan O’Brien‘s Christmas party Saturday night, loud enough for others to overhear. Rob and Michele left the party after the fight.

Hours after the party, on Sunday afternoon, Rob and Michele’s daughter Romy discovered their stabbed and bloodied bodies at their Brentwood house. Rigor mortis had already set in, meaning they had been dead for hours.

Romy is the one who called the police and told them her brother Nick — who’d been living at the house — was “dangerous” and should be considered a suspect.

Despite living there, Nick wasn’t at home when Romy made the discovery. Instead, he had checked into The Pierside Hotel in Santa Monica around 4 AM Sunday, using his credit card.

The reservation was made for just a day, but Nick never formally checked out.

When the staff came into his room later Sunday morning, they found the shower “full of blood” and blood on the bed.