My car and another were backing up at the same time. The other car was further out than my car. We connected and there is minor damage on the other car. The police officer indicates that fault lies on both our parts. Is this true?

Normally yes, if both are moving and both doing legal moves, it would be both at fault.
*** which is also a term for really no one and it is one of the true accidents.

Normally in these you pay for your damage, they pay for theirs, or your insurance may pay a part but not all of their damage.