The stepdaughter-in-law of Public Advocate Betsy Gotbaum died while in police custody in Phoenix following a heated argument with an airport-gate attendant, officials said yesterday.

Phoenix police said Carol Ann Gotbaum, 45, who lives in Manhattan, appeared to have strangled herself while trying to wriggle free from handcuffs while in a holding cell after the Friday incident.

Gotbaum’s husband, Noah, is the son of Victor Gotbaum, the former DC-37 union boss who is married to the public advocate.

“The family is in great grieving and stress,” Betsy Gotbaum told The Post last night from her home. “We have nothing to say. We hope that The Post and every other newspaper will respect our privacy.”

Carol Ann Gotbaum’s distraught husband, who answered the door at their Upper West Side townhouse, said, “I don’t want to talk about it. It’s rude.”

It was not clear why Carol Ann Gotbaum was in Arizona, but cops said she was traveling alone.

She arrived late for her U.S. Airways flight to Tucson and was told that the plane was preparing to depart, airline spokesman Derek Hanna said.

She allegedly began shouting at the gate attendant, and her persistent unruliness prompted the agent to call the cops just before 3 p.m.

“She became extremely irate, apparently running up and down the gate area,” Hanna said.

Gotbaum ran into the responding officers after going back through the security checkpoint toward the main terminal, said Sgt. Andy Hill, a police spokesman.

“The officers were not able to calm Ms. Gotbaum and eventually arrested her for disorderly conduct.”

Gotbaum resisted, and was “continually screaming” after being put into a holding cell, Hill said.

Officers checked on her every 15 minutes, but some five to 10 minutes after one check-in, he said, she had gone silent.

They then found that she wasn’t breathing and attempts to revive her failed.

“It appeared as though Ms. Gotbaum had possibly tried to manipulate the handcuffs from behind her to the front, got tangled up in the process, and they ended up around her neck area,” Hill said.

The Phoenix police are investigating.

Gotbaum, the daughter of a retired South African Navy commander, married Noah Gotbaum 12 years ago in Central Park.

Gotbaum and her husband have three young children, according to the Web site of a cellular technology company where Noah is on the board of directors.

Additional reporting by Bruce Furman