Each NJ municipality has its own rules, but I have never heard of an appraisal being required by any entity other than one that will be lending money (e.g mortgage, HELOC etc).

Are you selling and you want to know how much value the finished basement has added?

I think you are talking about a reassessment from your city. They will do this all on their own when the come for their final inspection.

I don't know but I love your screen name!