BMI vs. ASCAP Question

Our local theater group has asked me to be the sound engineer for their next play. One of my duties is to come up with the pre-show, intermission and post-show music. I found out the theater group has an ASCAP license, so I need to avoid BMI published music.

Is there a simple way to determine whether a piece of music was published by BMI or ASCAP? I went to the ASCAP website but there is no way I could find to query their database of published works.

You can search the ASCAP database here.

Thanks! Ignorance fought.