I have searched and found a couple others with this same problem, but no one has yet to be able to give an answer:

I parked my CLK320 outside, and came back about 20 minutes later and the car was making an electronic "cricket-like" sound coming from under the hood. Also when I opened the trunk to check out the battery, the light was pulsating very rapidly. When I got inside the car the tow-away light was also blinking. All of this ended up draining my battery so I had to get a jump.

As I said before I have seen a couple other threads with this same problem, but no one could find an answer including the dealer. Any help??

Other threads:

https://mbworld.org/forums/clk-class-w208/96818-clk-430-alarm-chirp-problem.html
https://mbworld.org/forums/c-class-w203/9468-help-please-read-ticking-sound.html

I don't know if I can solve your problem but I'll tell you what it is. a while back I fried my ignition. My car was on lockdown so I tried everything. I eventually set off the alarm, so when I got the trunk open I pulled the alarm fuse which as a precaution I assume began making that chirping sound. So I pulled the neg. battery cable, chirp chirp chirp, so I pulled the pos. battery cable, chirp chirp chirp. Turns out it has it own power source and it chirped like a happy and gay bird all the way to the dealer on a flat bed.
Check your alarm fuse in the trunk. When I put the fuse back the full loudass alarm went off and when I pulled it it chirped.