I took a new look at the car's anti theft system. I measured all wires to the Central locking pump and found something. The switch in the tailgate behave strange.
Photos and what I found here for you who want a closer look, page 7 and 8:
Chrysler Crossfire: Anti theft alarm
Note: there is wrong in the Chrysler schematics, they call the hood sensor for door sensor.
Next time in the garage I take apart the locking mechanism in the hatch. I have done that a couple of times earlier.
Thanks for all help !
Lars