Birth Certificate Enhancement Act of 2011 - Amends the Public Health Service Act to require the Secretary of Health and Human Services (HHS), acting through the National Center for Health Statistics, to provide such funds as may be necessary to support states in implementing the most recent versions of the Standard Certificate of Live Birth, the Standard Certificate of Death, and the Standard Report of Fetal Death and purchasing data from these vital records. Requires the Secretary to give priority to collecting statistics on infant mortality.