You still don't get the point. US police agencies can certainly be stationed and work outside the US. In this case they are there in an intelligence and investigative role. But, they do not have any police powers. They cannot make an arrest. What would your response be to a Dominican PN officer, who came up to you in NY City and said I'm arresting you and taking you to the DR for a fraud you committed. My guess is you would tell him to go f*ck himself. If he tried to detain you, you would scream "under what authority are you arresting me?". He has no authority in the US, the same for US police in the DR. The proper way this would be handled is for a warrant to be issued and the local police handle arrest and turn over to foreign custody at the border (airport)."NYPD's intelligence operations do not stop at the city line.
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Cohen* has also sent officers abroad, stationing them in 11 foreign cities. If a bomber blows himself up in Jerusalem, the NYPD rushes to the scene, said Dzikansky, who served in Israel and is the co-author of the forthcoming book "Terrorist Suicide Bombings: Attack Interdiction, Mitigation, and Response."
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David Cohen arrived at the New York Police Department in January 2002 (...) A retired 35-year veteran of the CIA, Cohen became the police department's first civilian intelligence chief.
donP