Jefferson County Magistrate William Senseney granted a continuance for the hearing. It is unclear when the hearing will be rescheduled, said Jim Kent, another public defender representing Dunlap.
Due to the "gravity of the charges," it is important that Dunlap have a psychological examination to make sure he is competent to go through with the court proceedings, Kent said after the hearing.
Delaney and Kent want to have Dunlap examined by Harold Slaughter, a psychologist in Martinsburg, W.Va.
Some of the people seated with the victim's family members were visibly shaken in court. When the group entered the courtroom, several Jefferson County Sheriff's Department deputies stood between them and Dunlap.
Dunlap's girlfriend, Jennifer Leigh Dodson, 20, of 308 New Oak Tree Court in the Willow Spring Farm apartment complex, was found dead inside her apartment on Feb. 19 around 9 a.m. Her throat had been cut, police said.
The apartment complex is off Prospect Avenue, outside Charles Town's city limits.
Dodson's sister and two friends found her body lying face down on her living room floor, Jefferson County Sheriff Everett "Ed" Boober has said.
The women had gone to the apartment to pick up a 2-year-old child Dodson was baby-sitting. Dodson's 1-year-old daughter also was found inside the apartment, unharmed in her crib, Boober said.
Boober said friends and family members told police that Dodson and Dunlap were having a relationship but Dodson had been trying to end it.
Dunlap, 45, of 312 Williams St., was hospitalized the same day Dodson was found slumped over the steering wheel of his pickup truck, which was locked and parked at the Princess Street boat ramp in Shepherdstown, W.Va., police said.
Inside the truck, police found two large kitchen knives, including one with blood on it, police said.
Dunlap was taken to City Hospital for treatment of pneumonia and was released last Wednesday. He was being held in the Eastern Regional Jail without bond.