There are numbers on the housing but the standard rear gear for the
250-300 hp 4 speed cars was  3.36:1. No it is not posi. All this is off
if someone changed the piece.

PDeen

Look for a sheet metal tag attached to one of the differential cover bolts;
if present it has a stamped 2-letter code indicating the ratio. I think
a 63 250hp
ordered with a 4spd would have come stock with a 3.08 non-posi., code "CZ".
If by chance it originally had a 3-spd (3,540 cars came that way, most
of them
probably 250hp) and the 4spd was added after purchase, it would have had
code "CA",
the code for 3.36 non-posi, the most common ratio in '63; "CB for 3.36
posi,
"CC" for 3.55 posi, "CD" for 3.70 posi., "CE" for 4.11 posi, "CF" for
4.56 posi,
"CJ for 3.08 posi, "CX" for 3.70 non-posi.
Don't ask me why they didn't just stamp the ratio plus a "P" where
applicable.

Or, place a chalk mark on the sidewall of a rear tire, at the bottom
(with the car on level pavement in neutral),
and another chalk mark on the driveshaft or a driveshaft U-joint where
you can see it if you look under the car.
Have someone slowly push the car forward for a count of 3 tire
revolutions while you scoot
along on a mechanics dolly counting how many times the driveshaft mark
makes a revolution;
divide the driveshaft revolution count by the tire revolution count and
you'll have the ratio.
The more tire revolutions you make, the more accurate this method would be.
3 tire revolutions would be 9.24 driveshaft revolutions if the ratio is
3:08, 10.1 at 3:36, 10.65 at 3:55, 12.33 at 4:11.
9 tire revolutions (multiply the above numbers by 3) would be about 27
3/4 driveshaft revolutions at 3:08 ratio, etc.
If you jacked the car up from beneath the differential and had 2 friends
rotate the rear wheels in unison
in the same direction, calling out the revolution count while you count
driveshaft revolutions as outlined above,
you'd accomplish the same thing, perhaps a bit more safely.... but you
may find that the half-shaft
U-joints have some interference when the rear wheels are hanging all the
way down