try using the file:///
protocol.
href='file:///C:mystyles.css'
If that doesn't work (and you say it doesnt), then my guess is that it won't work at all due to it being prevented by security features in the browser.
It depends on where you are loading the main HTML content from, but if the main HTML is loaded from the internet then I can understand why the browser might object to loading the CSS from the client machine's local file system.
One final thing to try: You might try setting up a web server on your machine, putting the mystyles.css file into the web folder, and loading it into the page using:
href='http://localhost/mystyles.css'
I can't really suggest much else, I don't think.
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