You are trying to set a release on a parent story. Parent/epic stories cannot be scheduled for release in UI or in WS API. In UI Release dropdown is grayed out on parent stories. When I try, I also get
{"OperationResult": {"Errors": ["Could not set value for Release: Could not set release for the parent object directly"], "Warnings": []}}
As long as you are setting a release on a leaf story it should work as follows.
Assuming: your user story ObjectID is 777 your release ObjectID is 888 your valid authentication key is abc123
URL:
https://rally1.rallydev.com/slm/webservice/v3.0/hierarchicalrequirement/777?key=abc123
and Payload:
{"HierarchicalRequirement":{
"Release": "/release/888"
}}