If everyone was a conjoined twin lawmakers would quickly get to work on taxing people by the brain, not the body. Same with voting.
The Department of Motor Vehicles would have to physically blindfold one head while the other took the drivers license test. In fact schools and universities would have to follow suit. This would enact a crisis as it would take twice as long for testing overall.
Enrollment in the military would drop drastically because both heads would have to agree to enlist. Joining the military would become mandatory, every citizen would serve 2 years in any branch.