I believe tomcat is not vulnerable to heartbleed out of the box.
Yes, the APR library is linked and SSLEngine is on.
<Listener className="org.apache.catalina.core.AprLifecycleListener" SSLEngine="on" />
But if you look at the server.xml config file of a default tomcat deployment, it's SSL connector uses JSSE not the APR library.
<!-- Define a SSL HTTP/1.1 Connector on port 8443
This connector uses the BIO implementation that requires the JSSE
style configuration. When using the APR/native implementation, the
OpenSSL style configuration is required as described in the APR/native
documentation -->
<!--
<Connector port="8443" protocol="org.apache.coyote.http11.Http11Protocol"
maxThreads="150" SSLEnabled="true" scheme="https" secure="true"
clientAuth="false" sslProtocol="TLS" />
-->
So it shouldn't be explotableexploitable via Heartbleed. Unless you manually changed the SSL connector to use APR, I think it's safe to say, you are not vulnerable.
Speaking of which do you know of any offline tester for heartbleed?
http://alexluca.com/2014/04/10/heartbleed-and-tomcat-out-of-the-box-ssl-config/
Regards,
Alex L.