The judge's comments came in the middle of jury selection for Hayes' trial. Jury selection was postponed pending a status conference Wednesday.
Officials wouldn't confirm a report by The Hartford Courant that Hayes overdosed on medication.
A Health Center spokeswoman declined to release Hayes' medical condition Monday.
Ullmann said he was trying to find out Hayes' condition, his prospects for recovery and whether he suffered brain damage. Citing a court-ordered gag order in the case and the confidentiality of medical records, Ullmann said he wants state police to investigate leaks to the media.
A state police spokeswoman said the agency was assisting the Department of Corrections, but referred further questions to prison officials. The department has declined to comment, citing the gag order.
Four jurors have been selected so far. Hayes' trial was scheduled to start in September.
Hayes and Joshua Komisarjevsky have pleaded not guilty to capital felony murder and other crimes in the deaths of Jennifer Hawke-Petit and her daughters, 11-year-old Michaela and 17-year-old Hayley. They face the possibility of the death penalty if convicted.
Hayes and Komisarjevsky are accused of breaking into the Petit home in Cheshire, beating Dr. William Petit, strangling his wife and setting the house on fire. The girls, who had been tied to their beds, died of smoke inhalation.