A dog is believed to have been killed by a blow to the head and stabbed following its death, after its owner let it out for exercise.
The Staffordshire terrier died on communal ground at Y Wern, Wrexham, on Thursday, 17 February.
Anyone with information can contact Pc Viv Jones on 101 if in Wales, 0845 6071001 (Welsh language line), or 0845 6071002 (English language).
Pc Jones said the owner was "devastated at the loss" and appealing for help.
"I would urge anyone with information regarding this incident to contact us immediately," said Pc Jones.