Does it state anywhere in the rules that you can't shoot your own ship?
Can you shoot your own ship?
Yes.
Step 1 of the Attack Sequence:
1. Declare Target: The attacker may measure range to any number of enemy ships and check which enemy ships are inside his firing arc. Then the attacker chooses one of his weapons to attack with. Then he chooses one enemy ship to be the target and pays any costs required for the attack.
From the FAQ:
Q: Can a ship choose to attack a friendly ship?
A: No.
Edited by Parravon
Such a shame, Dead Mans Switch would be so fun if you could.... MU HA HA HA../
you can deliberately bomb one of your other ships though 
you can deliberately bomb one of your other ships though
That's because dropping a bomb isn't an attack so it's not restricted by the rules for attacks.
Although, why you'd want to bomb yourself is beyond me. 
for the use of your dead mans switch
mmmm?
i guess is faster to drop the bomb directly, skipping the step of kill your own ship, isn't it?
maybe i'm wrong, btw
What you are looking for is Feedback Array, it will give your own ship 1 damage as well an an ion token and it will damage a enemy ship at range 1 then if it was your last hull point then you go boom, and dead man switch take over, damaging every ship at range one of the dead ship.
Problem is both are illicit so you can only use that trick on the shadowcaster I believe.
Edited by Torg