Wikipedia refers to splitting the baby as a legal term:

The expressions “splitting the baby” or “cutting the baby in half” are sometimes used in the legal profession for a form of simple compromise: solutions which “split the difference” in terms of damage awards or other remedies (e.g. a judge dividing fault between the two parties in a comparative negligence case).

But I suppose the judgment of Solomon would not work with cats.

A German judge, in Central Franconia of course, perhaps not a cat owner, tried two techniques to discover who owned a cat. First she took all the parties onto a car park roof and had the cat released to see who it would run to. The cat ran under a car, where it remained for a while. Secondly, she had both parties hold the cat to see who the cat preferred. The cat liked them both.

Auf Anordnung des Amtsgerichts musste die Frau die Katze nun zur Verhandlung mitbringen. Auf dem Parkdeck des Gerichts sollte sie das Tier dann frei laufen lassen. Die Richterin wollte damit feststellen, ob sich das Tier bei einem der Beteiligten zutraulich zeigt. Das ging jedoch schief, denn die Katze flüchtete sofort unter ein Auto und blieb dort auch erstmal. Erst nach längerer Zeit konnte sie hervorgelockt werden.

Eventually the original owner was able to prove ownership of Lumpele (‘Little Rascal’) with photos.

George Osborne, the Chancellor of the Exchequer, had his phone number put on Freya’s collar. See
I rescued George Osborne’s cat and put homelessness on the map. Freya was microchipped anyway, but this didn’t prevent her being looked after as a stray for three years some time earlier.

They gave up hope long before moving into Downing Street last year, assuming the cat had got lost – or worse, been run over.

So they transferred their affections to the family budgie, Gibson, named after RAF Dambusters hero Guy Gibson, and two goldfish.

It appears, however, that Freya is a better mouser than the original official mouser, Larry. David Cameron was obliged to dismiss him (he was more tolerant with Andy Coulson).

But microchipping doesn’t always prevent court cases.