It doesn't look like the ratio was ever established on the show, but it did appear in two high-profile sources. As you know, David Gerrold was the primary writer of the Season One TNG writers' guide (series bible), which established the overall count of 1012. He also wrote the novelization of "Encounter at Farpoint", and I quote from the Kindle edition:
The Enterprise had a larger crew complement than any of the other starships in the fleet—but the eight hundred included scientists and technicians of many types. The actual ship's operation crew was probably no larger than that aboard the old Constitution-class starships. There were also some two hundred noncrew aboard—spouses and children.
(According to Larry Nemecek's TNG Companion, an earlier version of the writers' guide, dated February 4, 1987, gave a crew of 907, so this total of 800 was probably left unrevised by accident. Still, it gives us a good idea of the intended ratio.)
The other source is the SciPubTech poster, which provides a detailed breakdown of 185 officers, 575 enlisted crew and 252 civilians = 1012. I'm not sure if this is consistent with the above by accident, but it is possible to check with the authors. They've often consulted with the Star Trek art department, so these numbers could've conceivably come from there.