Officers were called to the SPAR in East Ayton after a "heated verbal exchange" between a man and a woman inside the shop, which is also a Shell petrol station.
The argument happened on Main Street in East Ayton between 3.40pm and 4pm on Sunday January 16.
At this stage it is not known why the pair were arguing or whether they are known to one another.
North Yorkshire Police are now investigating and treating the situation as a "public order incident".
Officers are now appealing for information and witnesses who may have seen or heard the argument and specifically what was said by both the man and woman.
Anyone with information that could assist the investigation should contact North Yorkshire Police on 101, select option 2, and ask for PC 237 Glen Coates.
Alternatively, you can email [email protected]
Information can be passed on anonymously to Crimestoppers on 0800 555 111.
Quote the North Yorkshire Police reference number 12220008642.