I always thought that Prunella was exotic but it is listed as native in Newcomb’s Wildflower Guide. As it turns out there are two varieties and one is native (var. lanceolata) and one is not (var. vulgaris).  In the NYFA Atlas David Werier sets forth the history of this distinction:

Numerous early botanists recognized Prunella vulgaris as consisting of at least two taxa. One is considered to be native to North America (P. vulgaris var. lanceolata) and the other as native to Eurasia (P. v. var. vulgaris). Fernald (1913b) gives an overview of how these taxa have been treated in North America, provides a key to the varieties, and publishes the new combination P. v. var. lanceolata (W.P.C. Barton) Fernald. Fernald (1950) and Gleason and Cronquist (1991) follow this taxonomy while Mitchell (1986) and Mitchell and Tucker (1997) treat Prunella vulgaris as a non-native taxon without infraspecific taxa. A limited study from California (Nelson 1964) supports the distinction between the two taxa and also demonstrates support for a limited amount of introgression or hybridization at one California population. We follow Fernald in recognition of two taxa but a modern large scale study is still warranted. The North American native taxon (P. vulgaris var. lanceolata) has median cauline leaf blades ovate to ovate-oblong, 1.5-2.5 (avg. 2) times as long as wide, and rounded at the base. The Eurasian P. vulgaris var. vulgaris has median cauline leaf blades lanceolate to oblong, 2-5 (avg. 3) times as long as wide, and cuneate at the base (Fernald 1913b).

It would be nice to know if the distribution differs in range or ecology in New York so you might want to try to distinguish them in the field. Be sure to use the leaves in the middle of the stem for the measurements.  See the Atlas entry for the species HERE.