Mom has started calling the local sheriff's department when she's hallucinating (result of cognitive impairment). What to do?

Has your mom been tested for a UTI? That might be the problem. Rule it out if she will let you.

If your mother is refusing treatment/care and you are concerned for her safety, the State of NC has a system in place to have her Involuntarily committed and evaluated. They have facilities for over 65. The link posted shows a flow chart that indicates the procedure. It has a list of facilities and where they are located. It has the form you would need to sign and the steps to take.
Note it states outpatient treatment is available for those with someone to supervise them, otherwise inpatient. Don’t volunteer to help her if you know she isn’t going to cooperate.

You don’t say how old your mom is or what her comorbidities are or how severe her mental decline is. Depending you may be able to strongly urge her to take action to prevent you having to take this step. On the other hand, she might not be able to cooperate and needs this to help get her on track.

https://www.ncdhhs.gov/divisions/mental-health-developmental-disabilities-and-substance-abuse/involuntary-commitments

I hope it helps to know that this service is available.

Totally agree with BarbBrooklyn. If your mother has cognitive impairment and is hallucinating, she definitely should not be living alone. At this point she needs to be moved to a safe place, nearer to family. It's amazing to me that so many - my own mother included - refuse to open their eyes to the fact that they're aging and make arrangements for long term living.

If there's no PoA and she's too cognitively compromised to now create one (not that she even would be willing) then the ONLY outcome is that the county will eventually acquire guardianship and they will decide what facility she goes into and will manage all her affairs. You will no longer have any vision or participation into her medical or financial management.

You call APS to report her as a vulnerable adult to get her on their radar. Then contact her local police to tell them that any future calls from her social services also needs to be involved. You have no power in this situation if you are not her legal guardian and you can't convince her to cooperate.

Will her ltc policy cover in-home services?

If your mother has dementia and is having hallucinations, she should no longer be living alone.

Does anyone have power of attorney?

She needs to be transported to the ER the next time this happens and the discharge planners need to be told she can no longer safely live at home alone.

Are you in touch with the local emergency services? See them as a resource to get your mom the care she needs.