The police department discovered the posts on Wednesday, the same day the newspaper reported Dwyer would not be disciplined for past posts on MySpace, including "Some people are alive only because killing them is illegal."
The Journal reports his Twitter postings included a comment that he would pistol-whip the next person he hears saying "imma" instead of "I am going to."
Dwyer also posted that Muslims are like Chinook Salmon, "Life's great until the SEALS show up."
He could not be reached for comment.