Yes, the Crown also has a right to appeal a lower court’s decision, although this right is more limited than an accused person.
For example, unlike an accused person, the Crown is not allowed to argue that the lower court’s verdict on an indictable offence was unreasonable. Rather, the Crown may only appeal on the basis that the lower court decision made an error of law, such as by incorrectly stating the applicable legal principles.
It is important to have the assistance of a criminal appeal lawyer in order to respond to a Crown appeal, as you may be required to go through a new trial or even be immediately convicted of the offence you were originally found not guilty of.