The crime lab technician mislabeled samples, using “the victim’s name instead of suspect’s name,” her evaluation said. Her supervisors disqualified her from testifying in court because of her inability to “explain and retain basic concepts.”

Indeed, for a time, the technician, Serrita Mitchell, was only allowed to perform the most rote assignments at the New York City medical examiner’s office.

When she was given another chance, more errors occurred and she overlooked crucial evidence in a number of rape investigations, according to a new report by the state inspector general’s office.

The report describes a troubling pattern of mistakes at the city’s premier crime lab, also considered among the best in the country.

The inspector general’s office, which has already presented its findings to the medical examiner’s office, is expected to release its report Thursday morning.

The report was commissioned after The New York Times revealed some of Ms. Mitchell’s errors and efforts by the medical examiner’s office to determine the extent of her mistakes. It questioned the office’s application of a new method for interpreting complicated mixtures of DNA.

The method, known as the forensic statistical tool, is frequently used by the medical examiner’s office in cases where trace amounts of DNA might be found on a handgun that several people had handled.

But the report found that scientists in the medical examiner’s office often disagreed about how to read the results, sometimes overruling one another. Yet in those cases, disputes over the accuracy of the DNA analysis were never acknowledged in the case report shared with the district attorney, much less the defense lawyers.

The inspector general, Catherine Leahy Scott, said in a statement that such dissent should have been described in the case reports prepared for prosecutors.

Regarding Ms. Mitchell’s mistakes, the report underscores how much her supervisors knew about her “myriad failures,” but “did not terminate” her employment.

For starters, Ms. Mitchell regularly overlooked stains on the clothing of sexual assault victims, a lapse that meant crucial DNA evidence went ignored and untested.

In 2011, for instance, she was reprimanded after finding only six stains on a T-shirt and pair of jeans gathered as evidence in a sexual assault; a supervisor found 20 other stains on the clothing that should have been tested for DNA.

Even more troubling was evidence that Ms. Mitchell was not testing the few stains that she found, instead, in some instances, simply marking them negative for DNA. Her supervisors reviewing her work noted that it was an open question whether these were paperwork errors or whether she was “actually falsifying” test results.

For more than two years, the office of the chief medical examiner has been reviewing Ms. Mitchell’s casework. It has found discrepancies in the contents of 24 sexual assault kits that were a result of her misplacing evidence, sometimes returning it to an unrelated case.

The review also found 37 sexual assault cases in which she had overlooked evidence, preventing DNA profiles in some cases from being discerned until many years later.

In 2001, a 14-year-old girl told the police that an 18-year-old acquaintance had forced himself on her, but the case foundered. Ms. Mitchell was charged with examining the girl’s underwear for DNA, but none was found. In 2012, the evidence was re-examined and male DNA was discovered, leading to the man’s arrest.

The charges were ultimately dropped after the girl, now in her 20s, refused to testify.

In a statement, the medical examiner’s office noted that it had put in place numerous changes since the lab technician’s errors were discovered. “The inspector general concurred with the new policies and procedures we put in place, and found their recommendations to be valuable to our ongoing policy changes,” the office said.

Ms. Mitchell, who left her job in 2011, could not be reached for comment. Efforts to reach Ms. Mitchell at two telephone numbers were unsuccessful.

In examining the office’s use of the forensic statistical tool, the inspector general’s report cited a case of DNA taken from a gun in which the report examining the evidence “was rewritten six times” because of a dispute within the lab over how to interpret the mixture.

The disagreement centered on whether the DNA had come from two or three people; the answer would influence the degree to which a suspect was considered a likely contributor to the DNA mixture.

Despite having rules for how to resolve such disagreements, the inspector general found that a leading scientist at the lab, Theresa Caragine, had rewritten final reports and reassigned cases “when she disagreed with the findings” of lower-ranking analysts. No records of the disputes were ever given to prosecutors or defense lawyers. Dr. Caragine subsequently resigned.

The report notes that lawyers involved in the criminal prosecution who read “the final report would be ignorant of the dissension among the criminalists and Caragine regarding the case.”