As dictionaries go, you can't get much better than that towering giant of lexicography, The Oxford English Dictionary. It's always the first place serious word lovers turn when they have questions about the origins or use of a word. Yet really serious logophiles know its limitations. There are certain instances where you need to supplement the OED with a specialist work.

For example, the OED is not particularly helpful for Old English. It only records words that appear after 1100, so for words that drop out of the language before Middle English, you need to turn to something like the Dictionary of Old English or Bosworth-Toller.

Another area where the OED is not the most suitable resource is in researching dialectal forms. The OED does have some information on this, but it's generally not systematic enough to be helpful. As a case in point, consider today's Grammarphobia question, about the dialectal form dasn't and its connection to German-speaking communities. Pat notes the paucity of information about the form in the OED and continues with some informed speculation.

The Old English verb durren is a cognate (an etymological cousin) of the Old High German gitturan (to dare), which bears a slight resemblance to the modern German verb dürfen (to be allowed or permitted, to dare, to be likely).

That's the best I can do to account for the popularity of "dasn't" among German immigrants. 'Tis a puzzlement!

The thing is, she didn't need to speculate. The Dictionary of American Regional English has a thorough entry on dare, which includes numerous citations of dasn't and documents its idiosyncratic use in Pennsylvania Dutch communities. You can even see the entry with Google Books. (Search for dasn't).

The totality of the citations suggest that
(a) Early citations of dasn't aren't limited to German speakers or New England (the region with which the form is typically associated). Examples come from Missouri, Indiana, Tennessee, Alabama, Georgia, as well as New England. It appears to have become more limited in distribution by the mid-20th century.
(b) In the Pennsylvania German-speaking areas, dare (including the form dasn't) develops a special meaning may (not), for example, "Mom says I dassn't go out to play."

The DARE entry explains it this way:

B Sense
To be allowed [By identification with PaGer daerfe (Ger dürfen 1st and 3rd sg darfe), presumably originating in neg or interrog contexts where dare and may would be equally appropriate (see quot 1943)] PaGer area

So there's definitely a connection between dasn't and German speakers. The questioner's grandmother, who used dasn't, was born to German-speaking parents in Wisconsin in 1860. But no examples of her usage are given, so it's impossible to know if her usage was the more general 19th-century usage or one that is parallel to the Pennsylvania Dutch speakers.