Michael Gledhill, 44, was charged after police say officers found the 81-year-old Handy stabbed in the chest and unconscious outside his home in Los Angeles on Wednesday.
Handy was taken to the hospital and later pronounced dead.
Gledhill did not appear at an arraignment Friday in Los Angeles Superior Court and no plea was entered for him.
Superior Court Judge John H Reid ordered he be sent to mental health court and undergo psychological evaluations.
Another judge will then decide whether he is competent for trial.
Gledhill's lawyer Javier Trincado told the judge the sheriff's department decided Gledhill should not be brought to the courtroom, but did not provide a reason.
Trincado remained in court on other cases and was not immediately able to comment.
Authorities say Gledhill was arrested after telling police he was the person they were looking for.
Police had responded to the home after a 911 caller stated, "I am the son of man; I just killed the man of sin", according to the department.
Handy was a character actor in films and on television for decades.
Bail was set at $US2 million ($A2.8 million) for Gledhill, who lives at home with his mother, according to authorities.
Emails sent to Trincado and officials from the Los Angeles County Public Defender's Office were not immediately answered.
Born in New York, Handy appeared in films and TV shows for decades.
He was known for his role as an exterminator in the 1995 film Jumanji and more recently as the bartender Jimmy in the 2022 film Top Gun: Maverick.
He also appeared in some of the top TV crime dramas, including NCIS: Los Angeles, The Closer and Cold Case.
"I could not have asked for a more talented, humble or gracious client and friend than James Handy," Pam Ellis-Evenas, from the Ellis Talent Group, said in an email.
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