Electronic medical records are accessible across the country. Yes, they do have a vaccine database, and you can access any record through a state's IIS (Immunization Information System).

Enroll your child into any public school and you will be given an immunization record form to fill out. If there are any discrepancies between the squares you fill out and the records they have in this national database, you will have a school nurse calling you to tell you what immunizations are missing from your child's records. You can still opt-out of having your child's records made available on this database by way of signing another form, but it's only a matter of time before this will no longer be an option. Either way, it's looking like more states will be following the agenda behind CA and NY.