The Office of the Attorney General, which oversees the province's prosecutions, said on Thursday it needs to research its options for an appeal because of the strange circumstances of the case.
"This matter will be carefully considered to determine our next steps," said Brendan Crawley, a spokesman for the Attorney General.
Jan Luedecke, 33, was acquitted of sexual assault charges on Tuesday because he said he was asleep during the attack.
A sleep expert testified that Luedecke suffers from a disorder that causes sexsomnia -- involuntary sexual behavior during sleep -- which he had experienced before.
The court heard that Luedecke and the female victim met at a party. She testified she fell asleep and woke up to find Luedecke having sex with her. She pushed him away and called the police.
Luedecke confessed to police after he discovered was still wearing a condom and realized he had had sex.
Canadian media reported that the victim left the courtroom in tears when the verdict was read, and said she would take the case to the highest court possible.
The Crown has 30 days to present its appeal.