Telephone calls purporting to be from the kidnapers of a 15-year-old Vatican girl demanding the release of the man who shot the pope may be part of a hoax, police sources here said today.

After a day searching for a car in which a caller to a Rome television station said the body of music student Emanuela Orlandi could be found, police sources said they believed the call had been a fake. With all the publicity surrounding Mehmet Ali Agca, who is serving a life sentence for the May 1981 attack on Pope John Paul II, a kind of Agca fever seems to have evolved here.

The fuss was heightened last Friday, when Agca, who was brought to police headquarters for questioning about the Orlandi case, unexpectedly talked to reporters about the supposed kidnaping and about the attack on the pope.

Agca said he condemned the abduction, rejected all suggestions of an exchange and called for her release.

Speaking in Italian in what appeared to many to be a prerehearsed speech, the Turkish terrorist repeated the accusations he has made against the Bulgarian secret services for planning the attack on the pope.

Those charges form the basis for an Italian judicial investigation that has led to the jailing here for the past seven months of Bulgarian airlines official Sergei Ivanov Antonov.

The magistrate conducting that investigation, Judge Ilario Martella, left Rome yesterday for Sofia, where he is pursuing the inquest.

This weekend the official Bulgarian news agency said Italian officials deliberately had allowed Agca to talk to journalists in the courtyard of police headquarters so he could once again whip up what the Bulgarians say are defamatory charges.

It is not unusual in Italy for the press to be allowed to photograph or fire questions at prisoners when they are being transferred in or out of police headquarters, but it can be avoided if judicial authorities so decide, sources here have said.

Because of the notice attracted by Agca's comments about the Bulgarians, Italian Justice Minister Clelio Darida has ordered an investigation of why Agca was not kept quiet.

In Washington, U.S. officials said they assumed that the opportunity for Agca to talk to reporters was "not accidental," and said they are puzzled about the circumstances that allowed the contact.

The Orlandi case took another twist today after the Rome caller said the girl's body could be found in a dark red Ford Fiesta with a license beginning "Roma Z479" parked on Via Scinti. Police said the street does not exist.

In addition, the caller made no response to repeated demands by the Orlandi family for proof that she is definitely still alive, strengthening a growing conviction by Italian police that the girl's kidnaping is not the work of terrorists connected in any way to Agca.

Orlandi disappeared on June 22, and last week a man with a foreign accent began calling the press, the Vatican and the girl's family and friends to demand that Agca be released from prison in exchange for the girl's release.

On Monday it become known that the Rome branch of the Digos, the political police, have turned the case over to the city homicide office. Police sources say that the investigation is now concentrating on the possibility that the demands regarding Agca are probably a cover-up for something else ranging from murder to a secret romantic elopement.