The first thing to consider is what are we actually asking. It seems there are three different variables in our current discussion - assigned sex at birth, one's current sexual characteristics, and current gender/gender identity
Assigned sex at birth - female and male usually the only two options, as even intersex folks / folks born with ambiguous external genitalia are almost always still assigned one or the other at birth and have either male or female listed on their birth certificate.
Current sexual characteristics - basically, what genitalia and gonads does the person currently have or not have, which sex hormones are they exposed to and at what levels, and what secondary sexual characteristics are predominant for this person - these are things that could be captured in ICD codes / past medical and surgical history / current med list / asking the patient if needed.
Current gender identity - this is the variable that can get kind of tricky, as people may self-identify in many different ways. Common options include Male, Female, Trans Male, Trans Female, Genderqueer/Gender Non-Conforming or "Different" with an option to specify.
@owlegrad's doctor's office employ's the popular "two-step method" for collecting gender identity data - i.e., what sex were you assigned at birth, and what is your current gender identity? If you answer male for one and female for the other, that clues in your doctor that you may be transgender. Some folks who are transgender (in the sense that their current gender is not aligned with the sex they were assigned at birth) don't identify as transgender, so just asking on the form if someone is transgender is not an effective way to get the information you're trying to get. More on the two-step method and it's purpose is available here for your reading pleasure:
https://williamsinstitute.law.ucla.edu/wp-content/uploads/geniuss-report-sep-2014.pdf