Crawford Watch Company

The Crawford name shows upon Mikrolisk.

http://www.mikrolisk.de/show.php?site=280

The only information the listing gives is that the company was in New York. But you knew that. Not every name found on a watch dial is that of an actual watch maker. There are countless names of watch companies for every actual maker of watches. By far the majority of these anonymous watches were assembled from parts “off the shelf”, an obscure name printed on the dial, and the watch offered for sale. Hopefully, someone will come along with the information you seek, but for the moment, this is the only help I can be.