You can directly export cases from canlii.org into your Zotero library by using the Zotero Connector (address bar icon). Unfortunately, the Zotero Connector does not detect statutes from the CanLII website at this time.
The Zotero Connector turns into a set of scales when it detects a case. When you click the scales icon, Zotero will grab the citation information from the CanLII record, including the official print law reporter citation (if applicable) as well as other parallel citations, as shown below:
When you open the citation record in your Zotero desktop library, be sure to check it for accuracy and completeness. You may need to manually add or correct information in the record. Any parallel citations that were detected by Zotero are stored in a separate note, which is attached to the record as shown below:
The Zotero case citation template may not contain all of the fields that you need for a particular type of case citation, such as a neutral citation. One way to address this is to create a note attached to the citation record, and then manually add the neutral citation to the note, as shown below: