Dr. Elizabeth Morgan began serving an indefinite jail sentence yesterday after she refused to deliver her 5-year-old daughter to her former husband for a two-week visit. Her attorneys filed an emergency appeal with Chief Justice William H. Rehnquist.

Morgan, a McLean plastic surgeon, appeared calm and impassive during the brief court session. She spoke only once, to decline a request from D.C. Superior Court Judge Herbert B. Dixon that she disclose where her daughter is being kept.

"I'm not going to answer that," Morgan said.

Dixon then ordered her to jail "until such time as she produces, or someone on her behalf produces, the minor child," and U.S. marshals escorted her from the courtroom. Morgan has been ordered to pay a $5,000 fine each day she refuses to produce the child.

Morgan and her former husband, Dr. Eric A. Foretich, have been embroiled in a bitter custody battle since 1985. Morgan, who has accused Foretich of sexually abusing their daughter, has been jailed briefly twice before for refusing to produce the daughter for visits.

Foretich has vigorously denied abusing his daughter.

Neither Foretich nor his attorney, John C. Lenahan, were in court yesterday. Contacted late yesterday, Foretich said, "I'm concerned

bout the whereabouts and the safety of my daughter. Other than that, this is a matter between her and the court."

Dixon yesterday also instructed District police to start searching for the girl and to deliver her to the D.C. Department of Human Services.

Morgan is asking Rehnquist for a stay of Dixon's order until her appeal can be heard. The D.C. Court of Appeals denied a similar request on Thursday. Rehnquist had not acted on the petition late yesterday.

G. Allen Dale, one of Morgan's lawyers, asked Dixon to reconsider his decision, arguing that Morgan wanted to obey the law but felt compelled "to protect her child."

Dale said Morgan was convinced that her daughter, who turned 5 last week, would face the prospect of more sexual abuse if her former husband were permitted to have a two-week, unsupervised visit.

Dixon said he anticipated Dale's arguments, but he said the issue of whether to permit the visit had already been decided. Dixon said Foretich could argue in response that the child had previously visited Foretich during weekends and appeared to have enjoyed the visits. Also, the judge said, the child had "demonstrated affection during the visits and the child even resented going back home after some of the visits."

Dixon said he was being placed "in an untenable position" by Morgan's refusal.

"No person would voluntarily assume the responsibilities that I have at this time," he said.

Stephen H. Sachs, a former Maryland attorney general who is also representing Morgan on her appeal, said after yesterday's court session that Dixon's handling of the case was a "constitutional outrage."

Dixon, who refused on Wednesday to allow Sachs to join Morgan's legal team in Superior Court, has conducted most of the hearings in secret.

Dixon also has imposed a gag order on Morgan, Foretich and their attorneys.

"Because these proceedings have been closed, the public cannot know the strength of Elizabeth Morgan's case," Sachs said.