It's legit, I can vouch for it as I have the same bass (only mine's sunburst). It's the model Fender Japan called the '62 Reissue Jazz Bass (usually abbreviated as JB62), though I'm not sure why they called it that when not all of the features are specific to 1962; it's more like a '60s-themed Jazz with various features from the '60s combined. Mine was exactly like yours before I had parts replaced/added to be even more period-correct to '62
The following are accurate to '62 (early '60s in general)
- exposed grounding strip between the bridge pickup and bridgeplate (2nd pic)
- "offset contour" decal right next to the "Jazz Bass" decal on the headstock (3rd pic)
- bold font in gold lettering for the brand logo (3rd pic)
- template holes for pickup cover, and also for tugbar instead of thumbrest (4th pic)
Whereas the following are features introduced in the late '60s (possibly early '70s)
- single-slot bridge saddles (2nd pic) (early-mid '60s Fender basses had bridges with threaded saddles)
- generic tuners (3rd pic) (early-mid '60s Fender basses had 'reverse' tuners)
Unique to Fender Japan? (up till 2015)
- serial number at neck heel (5th pic)
The following are accurate to '62 (early '60s in general)
- exposed grounding strip between the bridge pickup and bridgeplate (2nd pic)
- "offset contour" decal right next to the "Jazz Bass" decal on the headstock (3rd pic)
- bold font in gold lettering for the brand logo (3rd pic)
- template holes for pickup cover, and also for tugbar instead of thumbrest (4th pic)
Whereas the following are features introduced in the late '60s (possibly early '70s)
- single-slot bridge saddles (2nd pic) (early-mid '60s Fender basses had bridges with threaded saddles)
- generic tuners (3rd pic) (early-mid '60s Fender basses had 'reverse' tuners)
Unique to Fender Japan? (up till 2015)
- serial number at neck heel (5th pic)