I think you are asking to get-logged into multiple sites (Joomla and
ur CI one..)
and normally normal DB setup doesnot provide that..
and you've to deal with session and cookies...
and there several other things (eg- Cross domain stuff)..
anyway U've come 2 the right place ....
with JConnect you can do this with Joomla and other applications
support JConnect..
What u've to done is make ur CI application as a JConnect external
application...
and how-to build that is briefly documented here..
http://code.google.com/p/jconnect/wiki/ExAppAPI
and of course u need get familiar with JConnect so follow the JConnect
development site & get familiar with it..
I'll help you to get this work done..
thanks..