Depends. They can cite under local and state law. Some localities have ordinances restricting drones. Some state laws are pretty extensive for aircraft laws and some aren’t. Then it also depends if you’re actually violating any of those ordinance or laws.
A good example would be deciding to flying after enjoying a bunch of drinks at a party to show off your drone. I’d wager money your state has laws that pilots can’t be drunk. He could charge you for a violation of that. A less example would be flying in a park that has drone prohibitions.
The FAA also accepts reports from local law enforcement. Let’s say you were flying an unregistered 1 pound drone in restricted airspace. Local and state laws may not have been violated but the FAA may get the report from local law enforcement and decide to issue fines based on that.
Above all, local law enforcement can physically write a ticket for anything at any time. It may not be a legal ticket and the violation may not even be true. It’s like how someone can sue anyone for anything, but there may not an ounce of truth to it. The proper way to address is through court. The improper way is to argue or fight with the officer and run the chance of getting more charges and/or looking like an idiot in court with body camera footage. There’s a chance that you may even find out you were in the wrong after further research.