If you have an emergency, call 911. When that is not needed but you need to contact the Sheriff's Department call 602-876-1853.
There can be issues that require a contact from the Sheriff's office but is not an emergency.
Some of these may include:
chronically speeding drivers
repeated sightings of transients (yes, it's unfortunate but many of them support their food and other habits by stealing from you)
Suspected drug activity
There can be many more reasons obviously but these are some off the top of my head. Remember, if we are starting to see accelerated suspicious activity and want more patrol presence that it is up to us to notify the authorities that we are experiencing these problems.