Thanks for the chance to help. I am an attorney with over 12 years military law
There is no rule that would require a service member to report an infraction. In the same way there is no rule that could require a service member to report a misdemeanor or felony arrest. Such a rule would violate the 5th Amendment right against self incrimination.
The only exception would be for individuals with high level security clearances (TS/SCI), who are required by the regulations that grant access to the materials to disclose arrests or charges to the security manager.
Now...despite the fact that there is not a rule requiring disclosure, it may well be in the interest of the member to disclose. If it is clear that the command will find out regardless, telling them up front can sometimes minimize the impact from the command. This is particularly true for more serious charges (where, for example, the command could press to separate the member administratively for misconduct...if they are going to find out regardless, best to tell them before they find out on their own)
For an infraction? That is a tough one. If there is a good change that the city will inform the base? I would recommend disclosure. But if that is not likely? There is no good reason to disclose. And certainly no rule.
Let me know if you have more questions, happy to help if I can