His lawyer argued Monday that Hayes, who could face the death penalty, is seeking "suicide by state" and is not competent to make such a decision.
A hearing will be held Tuesday in New Haven Superior Court.
Hayes made his statement after state experts said he was competent to stand trial. Defense lawyers have been concerned about Hayes' mental state since he tried to kill himself in prison on Jan. 30.
Joshua Komisarjevsky, 29, and Steven Hayes, 46, are charged with capital felony murder, sexual assault and other crimes in the 2007 deaths of Jennifer Hawke-Petit and her daughters, 11-year-old Michaela and 17-year-old Hayley.
They are accused of breaking into the Petit home in Cheshire, beating Dr. William Petit and holding the family hostage for hours before strangling his wife, Jennifer, and setting the house on fire. Michaela and Hayley, who had been tied to their beds, died of smoke inhalation.
Hayes and Komisarjevsky both pleaded not guilty. Hayes however, told New Haven Superior Court Judge Jon Blue at a competency hearing Thursday he wanted to change his plea to guilty.
Hayes could be executed if he is allowed to change his plea to guilty. The judge told him either a jury or a three-judge court would determine his sentence because he is not allowed to plead guilty to a death sentence.
A change of plea would have to be accepted at a formal hearing.
Jury selection has been ongoing in preparation for Hayes' trial, which had been scheduled to begin in September. Jury selection for Komisarjevsky is scheduled for January.