How to declare someone incapable of self-care?

Just because someone is incapable of self care doesn’t mean they are incompetent. If they are competent and of sound mind there is nothing you can do about it!! My 95 year old mother hadn’t bathed or washed her hair since last November 2019. I have been nagging her ever since. She finally let me give her a sponge bath and I used a shampo cap on her hair last Sunday. I didn’t ask her, I just did it. I walked up to her with a bath wipe in my hand. She knew I meant business!!

You would need to have a doctor's opinion that the patient constitutes a danger to him or herself. This danger could come from any number of sources. Inability to remember to turn off gas jets, for instance. Wandering and getting lost. So you need a diagnosis.
Short of this, let us say the person refuses to cooperate in an exam, if you have evidence that the person lives in unsafe conditions hygiene-wise (mold, dirty diapers, dead or dying animals, hoarding squalor), or if you know the person has been lost, is unsafe to drive, etc. You should call Adult Protective Services and ask that a case file be opened, explaining who you are, why you believe there is a danger.
It isn't enough to say "I don't think granny is a good housekeeper anymore, or granny isn't showering often enough" if you get my meaning.
With so little information from you it is difficult to see what is driving your questions, but I hope I have given you someplace to start.

Lindsaylane, not sure what your question is? Are you asking how someone is legally/medically judged to be incapacitated?