“We are still gathering evidence to determine the number of students who will be arrested,” Mr. Byrne said. “Additional arrests will include both those who paid others to take the test for them and those who created fake IDs and were paid to take the test for others.”

At the time of the arrests on Sept. 27, the county district attorney, Kathleen M. Rice, said she believed that impersonation and cheating were widespread. Mr. Eshaghoff’s lawyer, Matin Emouna, said the matter should have been handled by the school, and not the courts. “He has cooperated with the investigation, and he denies the charges,” Mr. Emouna said at the time.

Officials in the district attorney’s office suggested then that further arrests were imminent. Now, the office appears to be backing away from a specific time frame as it waits for information from the ACT.

Prosecutors face at least one major hurdle, officials said. A two-year statute of limitations applies to the kinds of charges that would apply to both accepting payment to take the test and paying someone else to take it. The arrests and continuing investigation have touched off a charged debate about security measures surrounding the high-stakes tests. At a State Senate hearing on Oct. 24, legislators and school officials criticized the College Board, which sponsors the SAT, and the Educational Testing Service, which administers the SAT, for lax oversight.

At the hearing, representatives of the Educational Testing Service said that about 3,000 test scores were examined for irregularities each year — out of more than two million exams taken — and that of those, 1,000 were canceled, most after test-center supervisors reported irregularities, or because of large jumps from scores on previous tests.