A fascinating and nerve-wracking encounter between a hiker and a curious black bear is likely to result in the animal being euthanased, park rangers in the US say.

Handheld video shot yesterday by hiker Stephanie Rivkin shows two black bears foraging for food beside a trail in Burlington, Connecticut.

The two bears are initially only metres away from Ms Rivkin but one steps cautiously closer as she talks to it.

"Don't be scared," she says as it eyes her.

"You look amazing."

The bear, which has already been tagged by wildlife authorities, eventually comes up to Ms Rivkin to sniff her leg, then shows its teeth as if to bite her, before stepping away.

"Oh, no, no, don't get crazy," Ms Rivkin says.

Sadly the bear is now set to be euthanased because of fears its overfamiliarity with humans could lead to it one day attacking a person.

Ms Rivkin told NBC Connecticut that she wished the bears could be saved.

"I had no idea whether or not I was supposed to be scared," she said.

"I just felt if I ran, I would be attacked."