A city overseer position is created by the Society (with input from the CO and local elders) when more than one congregation is in the city, even if there are only 2 congregations (as is the case in the town I live in). . The city overseer serves as a liason between the Society and the local congregations in matters involving all of the congregaitons. The city overseer's major responsibility is if there is a convention in their town and also serves as a "contact" for the media. A town north of me has 5 congregations. Until recently the district convention was held there and he was directly involved in those arrangements. A city overseer helps to coordinate territory borders between congregations within the city. If someone wants to know which congregation's territory they live in, they can call this brother. If there are foreign language groups/congregations in the city, they also are included in his area.
However, a city overseer has NO authority in any individual congregation in the city other than the one he serves in. Usually this brother is PO of the congregation he serves in and has many years, usually decades of experience. Usually this brother is a good communicator and a good consensus maker.
In my town, the city overseer position is a title only. Last thing this brother did was receive communication from the Society regarding the floods in this area about 15 years ago. He is not a good consensus maker...he ramrods his opinion down the throats of the elders in his and the others congregation.
Funny, there is not that much in print about this position. My info is insider info.
SnakesInTheTower (of the "hope this helps" Sheep Class)