Stepfather accusing me of stealing his tools. Any advice?

Your profile says that your mother has dementia, but it sounds like your stepfather has it as well, as paranoia is a classic symptom of it.
So you now have 2 people whose brains are broken and will never get any better only worse, so it's now time to educate yourself about the disease of dementia, so you're better prepared for the future. I always recommend the book The 36 Hour Day as a great place to start, and Teepa Snow(a dementia expert) has not only great videos on YouTube, but also some books she's written.
Make sure that both parents have their POA's in order before it's too late, and their living wills, and MOST forms.
Your stepfather is not out to get you, his brain is broken and he can't help what he's doing. You're going to have to step up and be the adult/parent now, and get used to living in their world as they can no longer live in yours. You have to be able to meet them where they're at, and remember that "logic doesn't live here anymore."(that's a saying we use a lot in my caregivers support group) There's a great book about dementia called Meet Me Where I'm At, that you may want to read as well.
You've got your hands full now with 2 parents with dementia, so I hope that you're getting "your ducks in a row" for their future care, and your sanity and self-care.

People cannot accuse you of theft if you are never there to steal anything.
However, a person with a broken brain will still be accusing you even when you are not there. It is not your fault. The Step Dad is ill.

In my experience, observing this happening to so many innocent persons:
1) The ill person seems to 'pick" one or two to accuse. It is a delusion maybe.
2) Keeping away from the accuser may be the only solution, at least to save your own reputation.

If both parents are placed together now, there may be several years of comfort left to spend together. Unfortunately, the adult children try to separate the couple, a fight ensues, family members choose sides, and it all blows up ending in a fight over inheritance.

Paranoia can be medicated.

Try not to force your Mom to side with your interests. Keep them together.

How sad and disturbing to be falsely accused, especially when you cannot fix it even by finding the lost object or clearing yourself with the facts.

My husband's mother has been accusing her neighbors for over ten years now.
Helpers come, and are accused. The money is later found in the freezer.

Have both parents assessed for needs, see if they can stay together, and medicated if necessary.

He has dementia and I hope for your sake that you do not live with them.
Your mother convincing herself that he's right likely means she has some kind of dementia too.
Him acting like he's the one setting you up when the tool is found, is most likely some showtiming.
Why is the niece doing the bill paying and not you? You are the son. I think you should have a talk with your niece and discuss POA with her.
What will probably have to happen is things will have to get a lot worse before anyone can act on behalf of your mentally incompetent stepfather and your mother. The niece should stop paying the bills. You should let them do whatever they want. Make sure to inform APS and ask the police to do wellness checks on them. If you live with them, make it your top priority in life to move yourself out. Otherwise your life will become hell on earth.
When they've made a big enough mess with their finances, selves, and home that is when the state will place them.

I would just encourage him to stick around with me when I visit. Hard to say at this point what is going on with him if this is the only symptom. If he is honestly HIDING them this sounds more like mental illness than dementia. No one with dementia is going to go through any elaborate hide and seek behavior. They might hide something and later not remember WHERE they hid it, at worst.

I would say he had Dementia. If not, why is he hiding the tools and then accusing you. Do u live with them? Have you recently moved in? Maybe stepfather doesn't want u there.

Has he been tested for dimentia ...my mother in beginning stages was doing that to us..saying we were taking everything ....or somthing else in that area? Maybe have him looked at ...just keep smiling best u can ...and they not to get each other arguing over it

I strongly suspect your stepfather has some cognitive issue.

My mother who had Alzheimer's did the same exact thing. Accusing me, my niece of stealing her money, her purse, her wallet, her this and that, etc. That stage lasted about 6 months to a year, but it was a terribly stressful time. I remember having to look for things she claimed were stolen and found them under the pillow, under the bed, under the mattress, inside her clothes in the drawers, at the bottom of the laundry basket, etc. It was crazy. My blood pressure was through the roof.

Paranoid thinking is not a normal part of aging.

Does your FIL have a formal diagnosis of any brain/thinking impairment? Alzheimer's Disease? Or any other 'label' of dementia?

Any other strange memory or thinking problems showing up?

Losing things is very common when short term memory starts to fade. Add some paranoia & blaming others happens. Sort of the brain's way of making sense of things. Really wild stories can happen too. *Confabulation* which can be sort of listened to but ignored. Hard when it is targeted at yourself though! Probably because you were more likely to use the tools than say your wife?

One tactic is to blame somthing/someone else.

One lady I met had about 10 purses. Her son bought them all in thrift stores. As each one was 'stolen' (actually misplaced, stuffed in drawers, under the mattress, in the bathroom etc) the son would find another one to replace it. Or he sometimes said the Police had caught the thief now, not to worry.