Is paying off mortgage public information?

Different counties could vary on what they report, but in my county there is a searchable public record when you file a mortgage on a property (including the mortgage amount) and when the mortgage is released. There is no public information on how the mortgage was released (or the payoff amount), so if the refinance is with the same institution, then there may not be any record of a mortgage release (since the mortgage was not actually released, just the loan refinanced).

A refinance with another institution could be inferred by the release of the mortgage on one date and a new mortgage filed on a nearby date. A complete payoff would simply be filed as a release of mortgage. There's no way that I can see to know if the mortgage was simply paid off or paid off part of a sale (although I suppose one could cross-reference the mortgage records with property sale records).

D Stanley's answer is excellent and just to provide information on different jurisdictions, I will explain how mine works:

Any time a lien is filed in my county, that is public record. So if you initiate any kind of mortgage, that information is available publicly and often generates a number of solicitations. Some companies are savvy enough to look back when your lien was filed, estimate your current pay off amount, and provide you with either a cash out refi option or a reduction in payments.

When a lien is released, it is not typically publicly available and does not generate solicitations.