I am (successfully) connecting to a database using the following:
java.sql.Connection connect = DriverManager.getConnection(
Nothing. Just execute your query. If the connection has died, either your JDBC driver will reconnect (if it supports it, and you enabled it in your connection string--most don't support it) or else you'll get an exception.
If you check the connection is up, it might fall over before you actually execute your query, so you gain absolutely nothing by checking.
That said, a lot of connection pools validate a connection by doing something like
SELECT 1 before handing connections out. But this is nothing more than just executing a query, so you might just as well execute your business query.