You shouldn’t have to. If your JDBC driver supports multiple connections, then the various createStatement methods will give you a thread-safe, reentrant, independent Statement that should work OK, even if other requests/threads are also accessing other Statements on the same Connection. Of course, crossing your fingers never hurts… Many early JDBC drivers were not re-entrant. The modern versions of JDBC drivers should work OK, but there are never any guarantees.
Using connection pooling will avoid the whole issue, plus will lead to improved performance.