On the subject of the local area police structure I went and ask a county sheriff's office about the set up in Georgia when I started writing Odd Man in College, and the outcome of their response and further replies is put together in the forward of that story, which states:
In most of the USA the head of the local law enforcement in an area is the County Sheriff, usually with a Sheriff's Office employing deputies to do the hands on law enforcement work. However, in some areas they also have city, metropolitan, and special police forces; such as a college police force. There are also differences in the law enforcement structure which varies from State to State. In each case they have authority only in their area of jurisdiction, and they then also have jurisdictional issues with matters that may also fall under the legal authority of the other law enforcement organisations like the relevant State Police Force (usually called state troopers) or federal agencies such as the Federal Bureau of Investigation (FBI), US Marshals Service, Department of Justice, Drug Enforcement Agency (DEA), Department of Homeland Security (DHS), Secret Service, and many others. In general they all get along and work well together, but not all of the people involved get on well with those from the other groups; this is especially true for some of the local - federal people's interactions, due to individual personal attitudes.
In Georgia, USA the Sheriff receives his law enforcement authority from the State Constitution, with approval to give this authority to Deputies. The Sheriff and his Deputies have county wide jurisdiction with some minor limitations, Police Departments receive their law enforcement authority through their elected local governing body which is authorized via a Charter from the State when a new city, county or authority is formed. Local Police Departments, for the most part, are limited to their legal jurisdiction under their authorizing charter. The Sheriff's Office is not a department under their county government, although they are funded through the county government.
The Sheriff is identified by the State Constitution as the county's Chief Law Enforcement Officer, but does not normally have direct authority over police departments who derive their police powers through a State charter. As of 2013 there are 159 counties in the State of Georgia. Only 12 have county police departments, but all are required, by the State Constitution, to have a Sheriff. The counties with police departments are generally in close proximity to large cities. In the remaining 147 counties without police departments the Sheriff's Office performs the police work in addition to their other State Constitutional duties.
The Henry County Police Department (HCPD) is responsible for handling the police activities in Henry County (unincorporated) areas that don't have their own police departments. This includes routine patrol functions, criminal and traffic investigations and enforcement. The Henry County cities of McDonough (the county seat), Hampton, and Locust Grove have their own police departments, and Stockbridge is in the process of forming one in 2013. HCPD does have shift commanders who are Lieutenants, while Captains and Majors are Unit Commanders.
The Henry County Sheriff's Office Deputies do enforce all the laws from serious crimes to traffic tickets, and they make many arrests in their county; so do the other city, county, and state law enforcement agencies within the county. However, the Sheriff's Office Deputies' primary Constitutional duties include: operating the county Detention Centres (jails); serving arrest and fugitive warrants, civil processes; providing security at the county court facilities, as well as the transport and guard of inmates to and from the courts; transporting inmates to prisons (after convictions), also to and from other jails for court appearances there. In addition to his required duties Sheriff McBrayer provides the School Resource Officers for the Henry County Board of Education county public school system, and provides personnel to assist other local and Federal law enforcement agencies (ICE, DEA and US Marshals).
In general, law enforcement agencies in the Atlanta Metro area work well with each other and share information, especially so when jointly working on cases. Deputies and Police Officers get to know each other through training, and by working together; so there is some sense of community. Sharing of the Law Enforcement Intelligence around the Atlanta Metro area is good, with Be on the Lookout alerts being emailed to surrounding areas. Also, many agencies post useful information on the Internet via official websites - like the Henry County Sheriff's Office website. Items like Most Wanted alerts and information about persons being detained in jails, etc. This saves people from driving to places to get basic information. There is also a network of information available to law enforcement agencies through local, state, and federal databases sharing and updating data from agencies anywhere in the country.
My understanding from later research is that this is true for most of the USA as well. While this doesn't give an exact answer for a very small community, I suspect the above is true for any community with a local law enforcement service, and a community without a local LE force will depend on the county sheriff's office and deputies.