Q. Is one allowed to appeal a decision by the planning board or does he have to go to Beis Din first?
You have two parties. Reuven and Shimon. Reuven applied to be able to build a building next door to Shimons house. While this building is not residential, and not typical for this area, it is allowed according to Township code however it does need to be approved in a case by case basis. The planning board approved the building plus a second type of building as well. While the Township code allows
the first type of building, the second type its not so clear if it is allowed (some lawyers say it’s not allowed), however the Township planning board approved it anyway. 
In this state, there is a method for appealing the Township planning boards decision. This appeal goes to the county level where a judge reviews whether it was supposed to be approved or not. 
So does this need to go to Beis Din before being appealed? 
A few reasons why not 
1) By Reuven applying for permission to change the use of the property to allow this building, he is bringing it into the non Jewish system already, so an appeal is just continuing what Reuven started 
2) Beis Din doesn’t have any jurisdiction over zoning decisions, so there is no din of arkoyos. 
3) The appeal is not against the applicant (Reuven) rather it is against the Planning Board, so it’s not two yidden against each other rather one yid against the Township. (and this is indeed how the appeal is structured). 
Or is it even with the above it is still something that one needs to get Beis Dins permission first before going into the non Jewish system. 
A. On question 1068 in regard to having to apply to a Beis Din or requesting a Posek to give permission to go to a Gentile court to challenge a landlord’s decision to keep a rent deposit wrongfully, we wrote;
Horav Shlomo Miller’s Shlit’a opinion is that you do not need permission from a Beis Din to lodge a complain for redress at the Landlord and Tenant Board or its equivalent. The reason is that enforcing established laws by applying to the corresponding authorities to make their decision if they apply and enforce them, is not considered going to court.
The Rov added that the above applies even when that decision is rendered by a government appointed judge to deal with these cases.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a