Can combat damage dice be assigned to a Death Star Under Construction (it has a black 4 listed as its health) or can it only be destroyed with an event too?

From my interpretation of the Destroying a Death Star section of the advanced booklet, the death star under construction can be destroyed in combat OR by using the Death Star Plans (it says the Death Star under construction CAN be destroyed by the death star plans, not that it must be)

However once construction is complete, only the death star plans will give the rebellion hope of destroying the second death star.

Under combat- next round (p 4 of rule reference), if the imperial player's only remaining ship is the Death Star under construction and the rebel player has ships in the system, the Death Star under construction is destroyed.

Under combat- next round (p 4 of rule reference), if the imperial player's only remaining ship is the Death Star under construction and the rebel player has ships in the system, the Death Star under construction is destroyed.

Thank you for citing! I somehow could not find this the other night.

Yes. Another way to get it off the map. I wonder how many imperial players are aware of the need to protect it while it's under construction.

It's a trap!

The DSC is a ship and has an armor type on health value and can be damaged like any other ship of that type.