Influencer Eugenia Cooney's very thin physique has resulted in her local police getting bombarded with calls and emails ... but we're told the YouTuber isn't in any sort of danger.

Concern for Eugenia's well-being ramped up in recent weeks after she posted TikToks of her dancing -- with many in the comments focusing less on the moves and more on her appearance.

A story also came out about her, sparking even more concern -- Greenwich Police Sergeant Brent Reeves tells TMZ ... calls and emails have been coming into his department about Eugenia from all over the world -- even getting people calling from as far away as Egypt and New Zealand.

We're told the callers are looking to make sure she's doing okay and isn't being forced by her mom to make content and keep up her appearance -- a couple of things that Sgt. Reeves says are untrue.

Sgt. Reeves says he's known Eugenia for more than a decade and they have a good relationship ... they even have a special code. She puts a certain object in her videos so he knows everything is alright.

If that object isn't there, however, he'll know to get her help.

The Sarge says Eugenia has always been skinny ... adding they can't really make her eat more if she's at the size that makes her comfortable. He says she's of sound mind and always has a bubbly personality when he chats with her.

Other agencies have checked on her in the past, but we're told she's never met the criteria to force her to get any kind of help.

This isn't the first time fans have been asking Eugenia to get help -- people have reached out over the years, notably in 2019 when YouTube star PewDiePie asked his followers to send her words of positivity.

She's also spoken out in the past about being put on a 5150 hold by her friends when she lived in California ... saying in 2020 she felt betrayed and ambushed.