A simple typo can slow down some good answers to your question. I am sure you intended to ask for "BioMetric" and not "BioMatrix".
There is something less heard of, Windows Biometric Framework (WBF). This is some information I found on MSDN, an article titled "About the Windows Biometric Framework API". Below is the link.
And regarding the database question, it depends on the way the API is used. If API methods are called and the validation is performed, then the results can be easily pushed to SQL Server databases using ADO.Net.
Hope this answers your question.