My father is constantly accusing my partner and children of stealing his possessions. What can I do?

Your profile says he is in "independent living and the primary ailment is alzheimer's / dementia." Sounds like his Alzheimer's is much worse and should no longer be in independent living.

Time for an Assisted living with lock down. Time for Dad to stop driving.

A person with dementia beyond the very earliest stage should not be living alone. And probably shouldn't be driving. Has his dementia been diagnosed? I'd call or write to the doctor who diagnosed him and explain his current behavior. The doctor may not be able to respond to you for privacy reasons, but still can listen to you.

He sounds like a threat to himself (living alone and driving) and a threat to you. Contact APS with your concerns. Explain that you want the best for him but you are concerned with him living alone, and about threats he makes to your family. They may not be able to do anything if they visit him and he claims everything is OK, but I think you should try.

Preferably time to get a GP involved or some sort of service.
Just a quick note to always remember you and your families safety. First. Every time.

He may have an infection/delirium and be unwell and thus behaving in such a way, but your safety is always important.
If you feel threatened or concerned by his behavior call an ambulance who can evaluate him and treat him if required.
Sounds very stressful.
All the Best.

Witsend, here is a good article to help you understand why your Dad is accusing you and your family of stealing. https://www.agingcare.com/articles/how-to-handle-alzheimers-disease-lying-144204.htm

Also, have your Dad checked for a urinary track infection as that can cause some strange behavior in elders.

You say on your profile that your father has dementia. And that he is living alone, and still driving, and his behaviour has now become abusive, threatening and dangerous.

Why, exactly, would you not want to involve the police?