In one of the all-time lows in American politics, the New York state Senate majority leader stood at a murdered cop’s funeral and chatted with his son on a cellphone about an alleged shakedown.

According to a federal criminal complaint unsealed on Monday, Majority Leader Dean Skelos was still at the January 4 funeral for NYPD Detective Wenjian Liu when his son, Adam Skelos, called him.

Dean Skelos was as cryptic as a wire-wary gangster as he relayed a promise that he is alleged to have just extracted from a senior Nassau County official while walking outside the Brooklyn funeral home.

“All claims that are in will be taken care of,” 67-year-old Dean Skelos was recorded telling his 32-year-old son.

Dean Skelos was apparently a little too cryptic.

“What’s that?” Adam Skelos asked.

“All claims that are in will be taken care of,” Dean Skelos repeated.

Adam Skelos finally got it.

“Oh, OK. Gotcha,” said the seeming Fredo Corleone of New York politics.

“All right?” Dean Skelos asked.

“All right, great,” Adam Skelos said.

“I’ll discuss the rest with you later,” Dean Skelos said.

The alleged grafting done for the moment, Skelos rejoined the mourning for one of two NYPD detectives who had been shot to death by a madman as they sat in their radio car just before Christmas.

Liu had arrived in America on Christmas Eve exactly 20 years before. He had spent his high school years hurrying from class to help his father finish piece work at a factory. He had studied to be an accountant in college but had been inspired by 9/11 to join the NYPD. He and his wife had been married for just two months and had been trying to start a family. He had died in the service of his city, state, and country before he could ever see a child of his own.

And here at the funeral was Dean Skelos, supposed grandee of the public trust, muttering on a cellphone what prosecutors say were assurances that his son’s grubby bit of graft was assured.

The alleged graft in this instance supposedly involved payments to Adam Skelos from an environmental services company that was angling for a water treatment contract.

“I literally knew nothing about water or, you know, any of that stuff,” Adam Skelos was recorded saying during another conversation.

Such corruption is sadly standard stuff for the New York state legislature, which has seen more than 30 members run afoul of the law in recent years.

Other purported dignitaries who attended Liu’s funeral included Assembly Speaker Sheldon Silver. He was arrested five weeks later on a federal criminal complaint charging him with fraud and extortion schemes that allegedly netted him almost $4 million.

Silver declared his innocence and tried to get the case tossed out, protesting in federal court that U.S. Attorney Preet Bharara had been grandstanding at Silver’s expense. The judge let the charges stand. Bharara proceeded to indict Silver’s son-in-law, Marcello Trebitsch, for allegedly running a $7 million Ponzi scheme.

Silver’s arrest seemed to put a fright into the Skelos father and son. Adam Skelos began using what he called his “safe phone” or “burner phone,” such as drug dealers favor. He seemed to imagine, wrongly, that it could not be traced and tapped. He was recorded grumbling to a Senate staffer that he could hardly “just send smoke signals or a little pigeon with [a] f---ing note [tied] to its foot.”

At one point, Adam Skelos advised his father that they should start communicating via FaceTime.

“Adam Skelos told Dean Skelos that he would explain during their FaceTime call why he wanted to use FaceTime,” the criminal complaint reports.

Skelos was recorded telling someone that FaceTime was preferable because the calls do not appear on the phone bill, “just the data plan.”

On March 28, the son complained to Dean Skelos that he could not obtain explicit “real advice” from his father.

“You can’t talk normally because it’s like f--king Preet Bharara is listening to every f--king phone call,” the feds recorded Adam Skelos as saying. “It’s just so frustrating.”

“It is,” Dean Skelos said.

At another moment, Dean Skelos was recorded warning his son, “Right now, we are in dangerous times, Adam.”

But they apparently still did not abandon the water treatment scheme, which allegedly involved funneling funds to the environmental services company from the $5.1 billion the state received in a settlement with Wall Street after the financial crisis.

“My best chance for being successful,” Adam Skelos was recorded saying of the scheme, adding that without it he would “lose the ability to pay for things.”

But all that just constituted yet another case of alleged corruption originating in the New York state legislature, one that, in terms of the supposed crimes themselves, is distinguished only by Dean Skelos’s stature as the person who, in his words, has the power to “control everything” in the Senate.

Beyond that, what marked this case as so much more shameful was the phone chat that the complaint describes as Skelos as having at Detective Liu’s wake but that, by the date, the craven pol in fact had at the funeral. The call became part of the evidence cited in the criminal complaint unsealed on Monday.

In a sorry coincidence, the next NYPD cop to make the supreme sacrifice was in his final two hours of life when Dean Skelos and Adam Skelos arrived at FBI headquarters in downtown Manhattan to be booked on corruption charges. Police Officer Brian Moore had been fatally wounded while placing himself in harm’s way with a selflessness that leaves crooked public servants in abject disgrace.

As they crossed the sidewalk Monday, father and son Skelos had their arms around each other in a familial embrace. You almost could have forgotten the charges against them.

After the arraignment, Dean Skelos declared that the allegations are groundless.

“I know that I will be found not only not guilty but innocent,” he told reporters. “I have absolute confidence and respect for our judicial system here in the United States of America, and utmost respect for our judges and our juries. And that’s why I will be found innocent and my son will [as well].”

The funeral for Police Officer Brian Moore is expected to be held in his home county of Nassau, also home to Dean Skelos.

But unless the Moore family wants him there, let us hope that Dean Skelos has already been to his last police funeral.