My battery died out and when i recharge my battery the alarm doesnt switch off. i dont have the manual and the alrm type is a autowatch auto car start

Call the Chevy dealer, even if you didn't buy it new or there. Also, and I learned this from experience, once an AC/Delco battery has been run down, they very often never work right again. I have bought 3 replacement batteries over the years because AC/Delco batteries are junk (fine unless you run them down).