punctuation - Punctuating a quoted question within a quoted statement

I'm working on a story, and I find myself faced with something of a quandary.

Specifically, I need to know the proper style for the following:

“I have thousands of them,” the commissioner answered, “but I’ll start with ‘What do you need?’.”

Is it proper form to have both the question mark and period, or should one of them be dropped?