I don't think there is a specific bylaw related to trees crossing into a neighbours property. The city only cares if it causes a problem on city land.
Unless the tree is deemed unhealthy and a risk to your neighbours property, i don't think you are legally obligated to trim it. couldn't find anything specific on the city of Calgary website, but i did find this article from Metro...
ttp://metronews.ca/news/calgary/2593...ee-in-calgary/