You need to be in Escrow by April 30th. So yes, you can close after April and still receive the tax incentive.
I wrote a blog about this recently with a handy chart. While the California column wouldn't be interesting to you, you may find the information on the Federal tax credit helpful:
So I would advise you to start looking if you want to get in a contract by April 30th. But at the same time, don't rush... you still need to find a place you will be happy in ultimately!
Keller Williams Realty