Hey Brian,
False positives do occur for unknown reasons, so it's possible that that's the case. It would be amazingly odd for you to have contracted hep C for any reason other than a blood transfusion before 92' or a needle stick. The only other real plausible possibility would be contracting it for your mother, which is perhaps an option to explore. Best of luck with all this, you will surely be fine in all aspects of this situation. Please keep us posted on the details, I'm very interested in the outcome of this.
In the US it would be illegal not to hire you pursuant to the disabilities act. With that said, some agencies do what they want, especially a police department. What you gotta do is focus on your health. See a doctor outside of police oversight and find out if you do in fact have HepC. Tell your doctor you want a complete liver panel done and tell him you want to know your genotype and viral load if you have HepC, I forget the name of the blood test. I'm sure it's important for you to be a police officer but nothing is more important than your health. good luck