See if this post helps:

http://ubuntuforums.org/showthread.php?t=44006

I followed the enclosed article. And when I am running the following command (which is not as a daemon. i just wanted to make sure it works before restarting):
I get the following output:
$ sh /etc/init.d/tomcat start
Using CATALINA_BASE: /usr/local/tomcat
Using CATALINA_HOME: /usr/local/tomcat
Using CATALINA_TMPDIR: /usr/local/tomcat/temp
Using JRE_HOME: /usr/lib/jvm/java-1.5.0-sun-1.5.0.15
touch: cannot touch `/usr/local/tomcat/logs/catalina.out': Permission denied
/usr/local/tomcat/bin/catalina.sh: 340: cannot create /usr/local/tomcat/logs/catalina.out: Permission denied

What security settings are required for it run properly?

OK... I modified the permissions and now tomcat runns perfectly when I initiate it from command line.
But I'm still unable to get it to run as a daemon.

Here is the script I put in the init.d dir:
#!/bin/bash
#
# Startup script for the Tomcat server
#
# chkconfig: - 83 53
# description: Starts and stops the Tomcat daemon.
# processname: tomcat
# pidfile: /var/run/tomcat.pid


# See how we were called.
case $1 in
start)

export JAVA_HOME=/usr/lib/jvm/java-1.5.0-sun-1.5.0.15
export CLASSPATH=/usr/local/tomcat/common/lib/servlet-api.jar
export CLASSPATH=/usr/local/tomcat/common/lib/jsp-api.jar
sh /usr/local/tomcat/bin/startup.sh
;;
stop)
sh /usr/local/tomcat/bin/shutdown.sh
;;
restart)
sh /usr/local/tomcat/bin/shutdown.sh
sh /usr/local/tomcat/bin/startup.sh
;;
*)
echo "Usage: /etc/init.d/tomcat start|stop|restart"
;;
esac

exit 0

Why doesn't it fire properly?