The self-signed root is probably okay, so long as that root cert is also in the Java keystore (jre/lib/security/cacerts -- not sure if jssecacerts is still used, but it probably is if you don't want to add anything to the shipped cacerts file).  The trust certs in cacerts varies based on Java version, so it's possible a newer Java will have the needed root certs. But if not sure, you can go to your jre/lib/security folder where your java runs, and if you have a jssecacerts file there, add your cert to it (and if it fails to add, you'll probably see that it needs some root certs added from the CA that issued your cert).
This is not really related to OpenESF, but to setting up SSL on Tomcat/Java, but the general idea is something like this:
- cd $JAVA_HOME/jre/lib/security
 - cp cacerts jssecacerts
 - keytool -import -alias certname -trustcacerts -file YOURCERT.crt -keystore jssecacerts   (not that certname should not be "tomcat" as that's special to Tomcat for finding the server cert it uses/presents for SSL and most likely you need to import your CA's root cert used to sign your SSL cert).  The default password for cacerts/jssecacerts is 'changeit' I believe.
 - Restart tomcat so it gets a fresh Java process running that will use the updated jssecacerts file.
 
Hope that helps...