Unless your address has changed, there is a good chance you will be able to renew OHIP without having to present documentation of your PR status. You may even be able to do it online.
Other than an initial application for OHIP coverage, I am not sure what might trigger being required to present documentation of status. Maybe if your address has changed, but I am not sure about this.
Personal experience (FWIW): Other than when I initially applied for OHIP, I have not been asked to present any documentation of my status in Canada for any of the several times my OHIP has been renewed over the last decade plus. I have not changed my address in all these years (been in this exact house for a decade and a half now). In fact, even though I have been a citizen for nearly a full decade, in my last two renewals I noticed that OHIP still shows me as a PR, something which I have been meaning to fix with OHIP but, well, I'm old and slow and tend to be a bit careless about such things.