According to the API documentation here, the Response header should include the etag. But when I look at the response headers, I do not see an etag, just this:
This seems to suggest the answer to your question is “documentation is incomplete / incorrect, but then the etag feature isn’t completed yet either”.
To quote from CH support (from Feb 2016):
I believe this (with info from other article) means:
The plan is to implement calling the API with an etag. Could be in the http header or as a parameter in the REST URI string.
If CH find from your etag that the resource hasn’t changed, CH will let you know. Presumably they’d return a parameter in the header as they’ve stated “no body” - but maybe you’ll just get no “body” in response…
If the resource has changed you get the resource in the body as you do now. The etag (always - I’ve not checked?) appears here.
For info, the documentation mentions an etag in the header for every REST call except:
The various searches
Registered Office Address
Filing History
Documents API (which is treated separately anyway).