Can someone explain what this means, does it mean the police is only part-time? 

The Franklin County Sheriffs office will respond to ONLY priority runs when Franklin Township Officers are off.
They will respond to injury accidents, robbery in progress, shootings, stabbings, domestics, etc… any other types of call, please wait until your police officers are working.

It means the Township police don't have officers on duty at night. County will respond to emergencies when the Township is off duty, but non-emergencies need to wait until Township police open back up in the morning. 

Common for very small towns that can't afford to employ extra shifts for a very low call load. 

If it's non emergent they aren't coming
Edit-protect your self

What are you missing here? The township is obviously tiny and doesn't have 24 hour service. When the township isn't providing service, the sheriff's office provides emergency response but won't take low priority calls.

They'll respond to life and safety calls but your burglary / theft / vandalism report will have to wait.

It means they're not coming out for non crimes, only for actual crimes like where someone is being hurt physically or under the threat thereof.
So don't expect someone to come out because your neighbor's dog is barking, but expect them if you shoot said dog.

Not part time but not 24/7 either.

They don't have enough officers to cover every shift. In a little town near me there are no "City" cops from 3 am to 7 am.

thanks - just needed confirmation if i read it correctly, i'm tired 

Franklin county nc?? I can see that bring the case with their sheriff's, my wife's folks live there and it's sparsly populated

Sounds like you're clear to take the law into your own hands.

It means the county sherrif's department isn't coming out to investigate your noise complaint at 3am. Call the township PD when they get in.

That means that the Franklin Township police department is running a less than 24/7 patrol.  They probably go home around 2200 or 0000 hours.  

We had a local municipality go pretty much non-existent during a really bad time in their department.  My department would actively patrol the city and answer priority calls but non priority calls were left for the couple of officers who were on during the day.

It's pretty simple. Some municipalities don't have enough for full time coverage.

If it's after hours get your own damn cat out of the tree.

Yep, PD it's self is not 24 hr coverage. Town next to where I used to be cop was like that at first. They used to not have a PD at all. The SO responded there and provided all LE services. If it was a priority call and no SO deputy in the area they would sometimes dispatch us until SO could arrive or we would back SO up in some cases. Then they got a Town Marshall. He basically worked days like 5 days a week during the day. Then a couple years later they hired a couple officers and a few reserves and had enough to cover 24 hrs 7 days a week. Franklin Township, my guess, only have a couple officers and not enough to cover some periors of time and the SO covers for priority calls. So if someone is wanting to file class C criminal mischief, littering or other minor misdemeanor,  not crimes in progress, they want you to wait until "normal hrs" contact the PD fo make a report. Crime in progress or serious priority type call they will respond.

Yep. That statement leaves me with zero questions.

Thanks all, just needed confirmation that understood it correctly. I didn't know there's actually part time police force, but with lack of money I understand.