Christchurch is considered to be a fairly safe city as it has a low level of crime, however various crimes can still happen so it's best to stick to well-populated areas. It's also a good idea to avoid places or situations that make you feel uncomfortable, especially if you're traveling alone or moving around at night. New Zealand is also located on a fault line so theoretically minor shakes and larger earthquakes can happen at any moment so it's always best to be prepared.