What version of ESLint are you using?
3.1.1
What parser (default, Babel-ESLint, etc.) are you using?
Default
Please show your full configuration:
{ "env": { "browser": true }, "parserOptions": { "ecmaVersion": 6 }, "rules": { "no-self-assign": "error" } }
What did you do? Please include the actual source code causing the issue.

var a = 123;
a = a;

var b = { a };
b.a = b.a; 

What did you expect to happen?
I would expect b.a = b.a to be a error;
What actually happened? Please include the actual, raw output from ESLint.
Only a.a is an error.

2:5 error 'a' is assigned to itself no-self-assign

✖ 1 problem (1 error, 0 warnings)