Smart Checklist emulates global Jira permissions by default as follows:
Users with "Browse Projects" only permission will be able to browse issues and see Smart Checklist content in these issues. They will not be able to bring any changes to checklists though.
Users with "Edit Issue" permission will be able to modify checklists (mark items as done/undone; edit items content, add/delete items, etc.), import templates and save checklist as a template.
Users with "Administer Projects" permissions are able to create/modify templates and set them as default. You can grant proper permissions via Project Settings → People → Add People
You can enable Custom Permissions to View Smart Checklist and Work with Smart Checklist. |
Go to Settings 
→ Apps → Smart Checklist → Settings → Permissions
Enable Custom Permissions by toggling these options:
Custom permissions to work with Smart Checklist 
Custom permissions to “View Smart Checklist”
With these permissions enabled you will be able to:
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Add Smart Checklist Items | Set status of Smart Checklist Items | Delete Smart Checklist Items | Manage Smart Checklist Items | View Smart Checklist |
add Smart Checklist, checklist items, save a template, apply template | check/uncheck checklist items, set statuses | delete checklist and checklist items | add new checklist items, edit, delete, change order, and import templates | view Smart Checklist and Smart Checklist History |
Go to Project → Project Settings → Permissions → Actions → Edit permissions
Look for the Smart Checklist permissions set.
Grant proper permissions to users/roles/groups in your project
Go to Project → Project Settings → Access → Manage Roles
On Manage Roles popup → Create Role
On Create Role popup → switch to App permissions
Find “Smart Checklist” actions
Give a name to the role (e.g.”Smart Checklist Creator”), select proper permissions
Assign the role to proper users or group and save it
For more precise information about permissions and their possibilities check this article → Checklist & Templates Permissions |