WASHINGTON — The Central Intelligence Agency has opened an internal inquiry into whether its close cooperation with the New York Police Department in the decade since the Sept. 11 attacks has broken any laws prohibiting the agency from collecting intelligence in the United States.

During his first Congressional testimony as the C.I.A. director, David H. Petraeus said Tuesday that the agency’s inspector general had begun to investigate its work with the Police Department “to make sure we are doing the right thing.” Mr. Petraeus said the inquiry began last month, but gave few details about its scope.

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