South Yorkshire Police have received "a number" of calls about a dog believed to have been stolen from a garden in Barnsley.
Anyone ringing with information needs to quote the crime number C/55050/2012 when they call police on 101.
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Bereaved parents were told that the council is concentrating its efforts on making sure it doesn't happen again.
The rheas, named Sally and Harry by staff looking after them at a farm in Haxey, were both found in the Sprotborough area.
It comes after months of protests following United Lincolnshire Hospitals NHS Trust's (ULHT) decision to close the unit overnight.