Officers were contacted at around 5.50pm on Saturday 8 March 2014, after two adults were seen being aggressive towards two boys who were with them in the car park of Creepy Crawlies, on Wigginton Road.
One of the boys was aged nine and the other was aged between three and four-years-old.
It was reported that the adults were using force towards the children which was unacceptable and beyond lawful chastisement.
Officers are appealing to anyone who witnessed the incident to contact them as soon as possible.
Anyone who can help the investigation is urged to contact North Yorkshire Police on 101 – select option 2 – and ask for Detective Constable Laura Wood or York Protecting Vulnerable Persons Unit.
Alternatively, information can be emailed to firstname.lastname@example.org
If you prefer not to give your name, Crimestoppers can be contacted anonymously on 0800 555 111.
Please quote reference number 12140037742 when passing information about this incident.