Through Sunday, the police reported a 2 percent decline this year in overall major crime.

The dispute underlined a fundamental dynamic of government statistics: The reality suggested by the numbers — whether applied to shootings, student test scores or the number of homeless people living in the street — does not always mesh with public perception. And the agencies that collect and keep the numbers are often judged by the public on the same statistics, increasing the pressure at all levels to report positive trends.

“This controversy highlights just how soft and subjective police statistics can be,” said Christopher T. Dunn, the associate legal director for the New York Civil Liberties Union. Referring to the new details on how shootings are tallied, he added, “This revelation suggests it is time for the Police Department to be much more transparent about the details of its statistics.”

Mr. Kelly suggested that the Police Department was undercounting shootings by not including some victims with graze wounds, or others who had been wounded by flying debris as a result of gunfire, but not by the bullets themselves. He questioned the number of recorded murders, saying some may be temporarily kept off the books by being declared still under investigation. He also questioned the logic of a reported decline in all shootings in 2015 while an increasing proportion of murders was committed using guns.

In its point-by-point written statement, titled “N.Y.P.D. Fact Sheet on Ray Kelly’s Comments,” the department noted an increase in homicides by gun this year, as well as a decrease in those by knife, describing each as “the normal ebbs and flows of crime trends in what is a period of historically low numbers.” Graze wounds are counted as shootings if they draw blood, the department said; glass wounds are not counted, and were not under Mr. Kelly.

Mr. Kelly said his information came from “several people” in the department. He said he was also told that some gunshot victims were logged as having “self-inflicted wounds,” which are not counted as shootings, if they did not cooperate with the police. The department said a wound is categorized as self-inflicted based on an investigation.

Mr. Kelly also said that more murders were being classified as “circumstances undetermined pending police investigation,” or Cuppi. That designation is temporary and “used at the sole discretion of the medical examiner,” said Julie Bolcer, a spokeswoman for the city medical examiner, adding there had been no change in the definition of the term. “Currently, there are 10 cases with the temporary Cuppi label that will receive final designations when the investigations are completed,” she said in an email on Wednesday.