Yup, WebAPI is your friend ! Native branch support is recent so the branch parameter is currently internal, but you may give it a go already (knowing that it may evolve in future versions). Just hit Show Internal API on the WebAPI documentation (embedded in your own server, linked at the footer), and check-out:
-
api/issues/searchfor any issue-related data (seebranchparameter) -
api/measures/componentfor measure data (seebranchparameter)