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More than 38,000 cops protect and serve the city of New York. By contrast, in the entire country, the FBI employs just 14,000 agents. And comparatively few of those are assigned to combat violent street crime.

These are facts the Trump administration must weigh as the president and the Justice Department design a federal response to the surge in crime that is plaguing major American cities.

Let’s draw important distinctions, from the federal standpoint, between what is possible, what is imperative, and what would be a prudent exercise of discretion.

First, what is legally possible. It is patently absurd to contend, as many have, that the federal government needs state government permission to conduct law enforcement operations within a state’s territory. The Constitution explicitly commands the president to see that federal law is faithfully executed. The FBI and other federal law enforcement agencies not only may but routinely do enforce federal law without even giving state authorities notice, much less asking for their approval.

But there is an important limitation: There must be a federal criminal law that justifies federal enforcement.

In our federalist system, policing crime within a state’s jurisdiction — particularly violent crime and property crime — is primarily a state responsibility. The feds, by contrast, may prosecute only if Congress has enacted a law based on some responsibility the Constitution assigns to Washington.

That brings us to what it is imperative for the federal government to do.

There are three broad categories of crime that trigger federal jurisdiction. The first two involve uniquely federal concerns: offenses against federal and foreign officials, and offenses committed on territory that, while located within a state, is not under state authority — e.g., U.S. military installations.

This is part of why it is ridiculous for critics to condemn President Trump’s dispatching of federal agents to protect such Portland sites as the federal courthouse. A critical federal mission is carried out in that complex. Moreover, it is a serious federal offense to attack the authority of the United States government by force. When federal personnel or federal property come under attack, the federal government does not merely have the power to act; it has a special responsibility to enforce the laws.

The third category of crime triggering federal jurisdiction is more complicated. These are offenses that ordinarily would be state crimes but concurrently qualify as federal crimes because they implicate important federal duties. For example, the Constitution assigns to Congress the duty to regulate interstate and foreign commerce. This empowers Washington to regulate the importation and distribution of drugs — both licit and illicit. Thus, virtually all narcotics trafficking crimes in the U.S. are federal crimes as well as state crimes. Guns, too, move fluidly in interstate commerce and are subject to extensive federal regulation.

Both drugs and guns are staples of gang activity and of street-level brutality. Congress has responded to this phenomenon by enacting an array of laws providing for federal investigation and prosecution: narcotics laws, firearms laws, racketeering laws, and so on. The racketeering laws are especially elastic: If violent crime can be tied to what federal law defines — capaciously — as a racketeering enterprise, then even crimes for which there normally is no federal jurisdiction (e.g., murder, armed robbery, gambling) can be prosecuted federally.

And so, finally, we come to the question: What would be a prudent exercise of federal discretion?

Plainly, there is no shortage of federal legal authority to investigate and prosecute violent crime. But there are severe practical limits on what the feds can accomplish in light of the modest number of federal agents compared to state, county, city and town police. How severe depends on cooperation.

If the federal and state governments work together, the impact can be dramatic — a boon for public safety, domestic tranquility and a flourishing economy. That’s why, in the most important federal enforcement areas, federal-state task forces have been established: for drug trafficking, violent gangs, organized crime, terrorism. The police agencies pool their resources, investigate jointly, and bring prosecutions in the court system — federal or state — that makes the most sense in terms of efficient process and appropriately severe sentences for the most culpable offenders.

In marked contrast, if out of political hostility state authorities refuse to work cooperatively with their federal counterparts, not much can be accomplished. Sure, the feds can make a big splash here and there with cases its agencies build unilaterally. But the feds are incapable of sustaining a long-term, intensive campaign against violent street crime on their own. Unless they are models of federal-state partnership, such efforts are doomed to fail.

It is a terrible thing for the country that Democratic politicians who control big-city governments have decided to signal solidarity with woke radicals by opposing all things Trump. It is atrocious that they prioritize defeating the president in November over working cooperatively with the federal government to suppress rising crime — which, they fear, might inure to his political advantage. That, nevertheless, is the hand we are dealt.

The president should continue holding the federal government out as ready, willing and able to partner with any state or municipal government — whether Republican- or Democrat-controlled — to confront surges of violent crime. But he should deploy federal police agencies, first, to address core federal responsibilities to protect federal property and officers, and second, to address violent street crime in states and cities where the local government wants to work with the feds against the bad guys.

Where left-leaning states and their progressive prosecutors are determined to spurn the feds, to the benefit of the bad guys, there is regrettably little the Trump administration can do. Federal agencies and prosecutors must soldier on with their work, of course — but it is best if Democratic government leaders are held accountable by other means for pursuing a political vendetta at the cost of public safety.

Former federal prosecutor Andrew C. McCarthy is a senior fellow at National Review Institute, a contributing editor at National Review, and a Fox News contributor. His latest book is “Ball of Collusion.” Follow him on Twitter @AndrewCMcCarthy.