Not in this instance. That statute simply sets out the default responsibility as between the two land owners. It does not bind anyone else. What it does is give you a claim against the neighbor if he/she does not pay his/her share. The county can make either one of you or both of you repair the fence. If you end up having to pay more than share, your recourse is to sue the neighbor for the excess he owes you by virtue of the statute.

