There is animal police in every district. Working from 7am to 7pm and after hours there is a response from the police stations. For Paphos the Main Switch Board is 26806530, 26806002 and if no answer then Nicosia main HQ 22808080 and ask to be put you through to the Paphos police station.
Also you can report to the District Veterinary office Paphos 26821260, 26821258. Other Veterinary Offices can be found here.