Shifting stances and a lack of clear standards from the governors of New York and New Jersey over their Ebola quarantine policy left critics and even some allies questioning on Monday whether the two men had fully worked through the details before they announced it.

In New York, local health officials said on Monday that they had not yet received any details of the three-day-old Ebola quarantine policy they are charged with enforcing.

In New Jersey, requests for such specifics were met with six sentences from a Friday news release.

Govs. Andrew M. Cuomo of New York and Chris Christie of New Jersey said on Friday that they were imposing their strict new mandatory quarantine because standards from the federal Centers for Disease Control and Prevention had been inadequate.

But on Monday, faced with criticism from the nurse who had been detained in Newark as the test case of the new quarantine, Mr. Christie said the C.D.C. — not New Jersey — had been responsible for hospitalizing her and giving her the Ebola test in the first place.