Found it.... I just had to look in the right section of the regs.

Species Defined as “Nuisance” Wildlife
Under the Code of Virginia (4 VAC 15-20-160) ten species are defined as nuisance species. These include:

Mammals
House Mouse (Mus musculus)
Norway Rat (Rattus norvegicus)
Black Rat (Rattus rattus)
Coyote (Canis latrans)
Feral hog (Sus scrofa)
Nutria (Myocastor coypus)
Woodchuck (Marmota monax)
Birds
European Starling (Sturnus vulgaris)
English (house) sparrow (Passer domesticus)
Pigeon (Rock Dove) (Columba livia)
Under state law, these species can be killed at anytime and in any manner that is legal under state and local laws (It is NOT legal to trap wildlife live and move it to another location.) These are the only species this applies to and a permit or hunting license is required to use lethal methods on other wildlife that becomes a nuisance.

You can take them anytime you want......