A Healthcare Project is constructing a new building adjacent to an existing LEED Certified hospital...

the local equivalent standard is more stringent than ASTM E1527-05

According to theLEED V5Reference Guide for Building Design and Construction, a Phase I ESA is required for all projects, except for those located on previously developed land that has not been used for industrial, commercial, or agricultural purposes. The Phase I ESA must follow the ASTM E1527-05 standard or a local equivalent. However, if the local equivalent is more stringent than the ASTM standard, then the project must comply with the local equivalent. Therefore, if the new building project is located in a jurisdiction that has a more rigorous standard for Phase I ESA than ASTM E1527-05, then it must complete a new Phase I ESA, regardless of the previous ESA done for the certified facility.

Reference Guide for Building Design and Construction v4 – Pages 81-821

LEED V5: Building Design + Construction Guide - U.S.Green Building Council2