PICASSO it aint but that hasnt stopped a finger painting by a classroom of kindergartners from sparking a big-money battle between an Upper East Side socialite and the posh Cathedral School of St. John the Divine.

Beautiful blonde-about-town Michelle Heinemann and her investment-banker hubby, Jon, have sued the school for $415,000 plus damages for allegedly conspiring to rig a fund-raising auction and then sticking them with a $50,000 bill for their "winning bid."

Trouble was, the dashing couple — whose son, Hudson Cornelius Heinemann, attended the school — had said they would bid only $3,000, tops.

"This is essentially a painting done by 5-year-olds," explained one source who knows the family.

The Heinemanns are so appalled by the school’s behavior that they pulled Hudson out and are now demanding compensation for all of the attending costs — including $20,000 tuition to a new school, forfeited class fees for his little sister, and Hudson’s $60,000-a-year chauffeur, whose job they want to save.

Little Hudson Cornelius was already an unhappy kindergartner before this incident, according to a lawsuit filed recently in Manhattan Supreme Court.

When he wasn’t residing with Mummy, Daddy and little sister Hyacinth Cornelia in their Fifth Avenue apartment — or in their waterfront manses in Dutchess County and Kennebunkport, Maine — young master Hudson was getting chauffeured to the Upper West Side private school, where tuition runs $39,000 a year.

The tousled-haired tyke was "underappreciated” there.

"Plaintiff’s son was consistently left out of school exhibits and films . . . and was made to go last at nearly everything," the lawsuit states.

"On one occasion, plaintiffs’ 5-year-old son was relegated to the role of 'door-holder’ and ordered to hold the door for all of the other students."

School administrators, including Principal Marsha Nelson, agreed to speak to the boy’s teachers, and on that assurance the Heinemanns gave the place another chance and made a couple more goodwill donations — including to the March 1 school fund-raiser charity auction, the suit alleges.

The Heinemanns donated $6,000 worth of "designer clothing items” to the auction, and Michelle — a "renowned artist" whose paintings have been shown internationally — worked with Hudson’s class to create a sellable work of art.

The painting consists of the traced-and-cut-out paper hands of Hudson and his 17 classmates, all painted and affixed to paper, along with each child’s written answer to the question, “How do you feel when you are around art?"

Told that such paintings typically sell at school fund-raisers for $500 to $1,200, the Heinemanns said they couldn’t attend themselves but would be happy to place the winning bid — up to $3,000, the suit says.

But the school’s director of advancement had a first-grade teacher named “Ms. Bryant” drive the bid up to “the outrageous sum of $50,000,” the suit alleges.

"The Heinemanns tried to settle this matter without a lawsuit, but the cathedral had no interest in taking responsibility for their actions," said family spokesman R. Couri Hay.

Officials at the school did not return repeated phone calls yesterday.