You could gently scrape with your fingernail, a little bit of the stem. If it shows green, then it isn't completely dead. If so you could try cutting it back then waiting for shoots to appear.

Do as Mad says - if the stems are obviously dead, pick off a small piece of bark on the mainstem nearer the root - if that's dead too, then its most likely completely dead. Otherwise, its just wait and see if it shoots again.

Bottlebrush frequently comes back from stumps, but it may be a year or two before it blooms again.