Dates don't just specify when you signed a legal document. They can be central elements in contract provisions that state when conditions must be fulfilled and when payment must be made. But while it is important to be accurate when specifying dates, you don't have to worry much about writing them in any particular way.
In yesteryear, when legal documents were drafted with great formality, dates were written out both in letters and numbers. This precluded the possibility of a small error causing big problems. The system is still used for writing checks, and some banks and agencies continue to use this format for property deeds.
Under modern rules, few if any states limit how you write dates in legal documents other than requiring standard American usage: the month first, the day second and the year last. Some attorneys spell out the month and use numerals for the day and year, while others use all numeric numbers. Spelling out the month eliminates confusion if dealing with other countries where the day comes first. As long as the intent is clear, all forms are acceptable. In standard form documents, a blank space is generally left for the date to be filled in by the person completing the form.