Should I screen my patients age 27 through 45 years for previous HPV infection to determine whether to offer them HPV vaccine?

No. No screening laboratory test can determine whether a person is already immune or still susceptible to any given HPV type. Most sexually active adults have been exposed to one or more HPV types, although not necessarily all of the HPV types targeted by vaccination. HPV vaccine works to prevent infection with vaccine types to which a person is still susceptible.