The precipitation type (formerly called the hydrometeor classification) is one way to check the contribution of birds to a radar image. Although called called Precipitation Type (rain, snow, hail etc.), one classification under this heading is biological and includes birds, bats and insects.
Note: Precipitation types are interpretations of the radar signal produced by a computer algorithm. It is possible that the classification is wrong sometimes, and I know of one such apparent error. On one cold, cloudless fall night in Albany, New York the reflectivity signal looked and behaved like migrating birds, but the precipitation types were mainly snow and ice crystals.
In addition to the National Weather Service website you can view the classifications at the College of DuPage weather site. To use this page, click on Radar Site Map at the top right and chose your radar site, and then go to the Product Menu at the top left and choose Hydrometeor Classification --> Current at the very bottom of the list. Precipitation types can also be viewed with RadarScope, an app for Android and Apple mobile devices.