In an unhappy feat, an Upper West Side mom says her ice-skating daughter was injured because Bryant Park rink staffers refused to give her a “safety penguin.”

Brigitte Casper rented skates for her 5-year-old, Ida, in November and took her out on the rink at the park’s Winter Village, repeatedly asking employees for the penguin — a plastic balancing aid that kids can hold in order to stay upright.

But the workers refused, claiming only children age 4 or younger could get the penguins, Casper claims in a lawsuit.

Staffers didn’t understand their own rules, the exasperated mom insisted. The criteria for getting a penguin was a kid’s height, not age, she pointed out in a Manhattan Supreme Court legal action filed last week against Bryant Park.

The employees wouldn’t budge, and Ida was “seriously” injured in a fall, according to court papers.

Casper is seeking unspecified damages.