Would a string of murders, assumed to be cult-related, that all occur in the same city, fall under the jursdiction of the FBI or local police? I don't think my local police would be too happy if I called and asked...
If you go to the FBI's webpage, they get a little more detailed, but from what I've read they will assist local law enforcement - I know on TV they say they have to be invited, but I didn't read enough from the site to confirm that. But definitely check their website.
It's under local jurisdiction unless there are federal crime elements involved. If one of the victims is a federal employee, it could fall under FBI jurisdiction, or if there is a strong connection to a case already under federal investigation. If a national bank is robbed as part of the crime, or an armored truck assault, it will probably fall under federal jurisdiction. But federal jurisdiction isn't only FBI. There is also the Department of Justice or Treasury or the ATF who could be in control. Jurisdiction can be a mess, and the local police don't always look kindly upon federal "interference."
if it was a 'hate crime' that could also fall under fbi jurisdiction, since that is a federal offense... same goes for if the cult has any connection to acts of terrorism, which would put it under the homeland security aegis and involve the fbi...
I would suggest you actually go in and talk with the local police department. Explain that you are researching information for a book and see if they have anyone available to talk with you for a bit. The worst case is that they give you some odd looks and say no, best case is they are intrigued and have someone that has some time.