This is a complicated question with many possible answers that depend on many factors. Usually this will be considered a property owners dispute where your rights for access and their rights for being the land owner are needing to be determined, in these cases Navajo County will not become involved, talking with the neighbor or having someone arbitrate the issue may help resolve the problem. If that does not work, then a judgment could be sought.
Navajo County has jurisdiction over County Maintained Roads, and oversight over publicly dedicated roads and easements within the County. If there is no easement, convoluted documents, or if private; then again, Navajo County will not become involved and considers the issue a property owners dispute. Administration cannot be used to determine between different rights of different people.
If the easement or ROW is dedicated to the Public, then please contact Navajo County Engineering Department and explain the issue. There are some things acceptable and other that are not acceptable. If on a County Maintained Road, please contact the Road Yard as they have the responsibility to ensure the welfare of the traveling public on County Maintained Roads.
We highly recommend that the legal status of the roadway in question be thoroughly researched prior to installing any gates or fences on a road in the County. By researching and communicating with those who may be affected ahead of time, many issues can be solved and the process will be much simpler.