Yes, the first documented instance of this was with the Mongolians. They catapulted bodies infected with the bubonic plague over walls, when at war with Crimea. It was widely theorized that they are responsible with actually starting the imminent spread of the plague and were the first to utilize the terrors of biological warfare. Source: http://wwwnc.cdc.gov/eid/article/8/9/01-0536_article

Yes, there were also seiges where armies launched poisonous snakes and scorpions as well. The only problem with this type of warfare was that you had to enter the city after you won.