A news release from the office says RCMP in the Vancouver Island city notified the IIO, less than an hour after the Saturday morning incident.
Investigators were told police spotted a man and women allegedly fleeing from a stolen vehicle at about 2:30 a.m. on April 27.
A police dog was used to round up the pair and both were bitten, requiring medical treatment.
A report to the IIO was submitted by 3:30 a.m. on Saturday and two members from the office arrived in Nanaimo later that day.
The Independent Investigations Office examines all matters where serious injury or death results during cases handled by any police agency in the province.
Note to readers: This is a corrected version. An earlier version listed the date as April 26, and the time of the incident as 10:40 p.m.
Also on HuffPost