I don't believe it will fit. The CRX and Civic bumpers are definitely different.

There was a place I used to be able to check part numbers, but the site doesn't seem to be working at this time, so I can't say I'm 100% right about this.

I know that there is a difference in the years also. I've found that an 88-89 CRX lip will not fit a 90-91 front bumper. I've been trying to get my hands on a lip for my 90-91 bumper for a while now with no luck. Too bad you don't live closer