Yes, some ladybugs may bite. In particular, the multicolored Asian lady beetle, while not aggressive toward humans in general, has been reported to bite. Though they are not poisonous, the bite may hurt and develop a red mark.
Imported into Georgia from Japan in order to control pecan aphids, the multicolored Asian lady beetle is not typically considered an indoor pest. Though they attempt to enter structures during the winter, they do not eat or mate during this period. These lady beetles do not carry disease, nor do they eat wood, buildings or human food. Instead, once spring arrives, they leave their shelter to seek aphids and soft-bodied insects to consume outside.