I haven't done it yet (pre-op), plus I was born in Ontario so that's where I would have my birth certificate changed. I had thought that the trans health website had some info on it, but it looks like they've re-organized and removed a bunch of stuff (should've downloaded it all when it was still there).
Anyhow, I found this (at
http://sagatucson.org/downloads/BirthCertificateChanges.pdf). I don't know how up to date it is, but contacting vital statistics BC for current info sounds like the way to go.
Sex on a birth certificate issued in BC can be altered if 1) the sex was recorded in error at the time of birth, or 2) the
person has undergone SRS.
The applicant must provide a certificate from the physician who performed the SRS; evidence that the physician is
licensed in the jurisdiction where the surgery was performed; and a certificate from a physician licensed to practice
in the jurisdiction where the applicant resides, stating that the person has completed SRS. (The government does
not require a specific type of surgery to be performed, but that the physicians certify that the sex has been reassigned
according to accepted medical standards).
Formerly, the applicant had to be unmarried; now that same-sex marriage is legal in BC, this requirement is no
longer enforced. The fee to amend the birth certificate is $27.00; if a new certificate is to be issued, there is a fee of
$27.00 for that service as well.
A person may change their name to one appropriate to their gender of identification without undergoing SRS or
changing their legal sex assignment.
Pleas see: BC Vital Statistics Agency for details.