Back up battery installation

I'm looking at installing a seperate battery for my alarm in my trunk. How would I go about hooking up the battery so that it recharges?? It's going in a 2002 Dodge Neon R/T. Can I run the pos. wire from this battery parallel with the stock battery then ground it in the trunk? Also I've heard that installing another battery will cause the other one to discharge, fact or myth? 1 last thing, what size fuse should I use for the power wire??

If all you plan on running off that spare battery is your alarm then yes you can run them in parallel. Now as far as installing another battery will cause your main one to discharge there is some fact to that.  Look at it like this you have 2 water tanks their drain pipes go into a Y. So you’re getting the same amount of water out the Y but you have double the water reserve as you would with a single water tank. Now think of the water as Amp’s. Now you can isolate the batteries with a battery isolator which will allow you to drain your alarm battery while allowing your primary battery to maintain a full charge. However an alarm dose not draw that much current.  You should not need a 2nd battery but if you wish to add one you should not have a problem running them in parallel without a isolator. 

Thanks for the reply. The reason why I'm adding a second battery is because, I am putting in some mini piezo sirens inside my car. Sure battery back up sirens would kick in outside if the main battery is cut but then the piezo's would stop since there is no battery back up. If I have a seperate battery then if they cut the main battery the piezo's still have power going through to them from the back-up battery.

DEI sells a backup battery for alarms, small and compact fits under the dash and has .7 amp hours, enought to run a few peizo for about 5 mins also it will set off the alarm when battery power is diconnected as long as your alarm uses negative triger inputs. $30 if you want one.