Jira REST API. Read/Write checklists
You can use Jira REST API to work with the checklists.
Now the Smart Checklist dedicated REST API is available! For more complex use cases and integrations - follow the instructions Smart Checklist REST API v1.0
Overview
You can read/write checklists by using Jira REST API accessing a Checklists custom field or com.railsware.SmartChecklist.checklist issue property
Read more about custom fields used by Smart Checklist addon and their setup here: Custom Fields Setup
Method  | API reference  | 
|---|---|
Get checklist value rom existing Jira issue  | Use the Get Issue Jira REST API  | 
Create Jira issue with the checklist applied  | Use the Create Issue Jira REST API  | 
Set the checklist for existing Jira issue  | Use the Edit Issue Jira REST API  | 
References
Checklist Format
Use checklist RAW text Markdown format to set its value. Check the Formatting Guide for more info.
Example
Set the checklist
"customfield_10001": "- ToDo List\n+ Checked\nx Skipped\n~ In Progress\n# Another ToDo List\n- Unchecked\n> Quote line 1 https://rw.rw\\n> Quote line 2\n> Quote line 3\n"Custom field id customfield_10001 might be different on your instance. Make sure you use the correct one. 
Here’s How to find id for custom field “Checklist” on Jira Server and Data Center.