The image retweeted by Stephen Moore is meant to compare the premier to the television character "Dexter," who is a Miami forensics expert by day and a serial killer of criminals at night.
The photo of the premier has been altered to show him with stylish blonde hair, sideburns and wearing an open-necked shirt.
The NDP issued a news release saying the retweet of the image was a new low in the four-day-old provincial election campaign.
The party says the image is a childish barb and has asked Liberal Leader Stephen McNeil to apologize for his staff who redistributed the image.
"Mr. McNeil should apologize for the actions of his campaign team in distributing the photo and he should apologize for his director of communications who said the image was 'appropriate,'" says NDP candidate Maureen MacDonald in the news release.
Kyley Harris, the Liberal party's director of communications, says he also tweeted the image and there will be no apology.
He says the image wasn't created by the Liberals and the party doesn't necessarily endorse it.
However, Harris says the reason staff retweeted it was because they found it was making a valid point in a light-hearted way.
"I looked at the image and it seems to be a pun, a play on the name of the premier who has had some trouble keeping jobs in the province," said the spokesman.
"I believe it's a light-hearted pun on a popular show and a premier who share the same name."