Building Efficiently Act of 2019 This bill amends the Internal Revenue Code to expand the new energy efficient home tax credit to allow, in lieu of the existing credit, a credit for 3.3% of the cost of constructing a new energy efficient home that is a qualified energy efficient residential rental property. An energy efficient residential rental property must be certified as being constructed, reconstructed, or retrofitted under a plan designed to reduce energy and power consumption of the building by at least 40% compared to (1) the baseline annual energy and power consumption of the building in the case of a retrofit made to an existing building, or (2) a reference building which meets the minimum requirements of the International Energy Conservation Code 2018 in any other case. The bill also (1) extends through 2020 the energy efficient commercial buildings deduction; and (2) eliminates the basis reduction requirements for certain low-income housing properties receiving the energy efficient home credit, the energy efficient commercial building deduction, or the credit for investments in energy property.