In fact it will need 7 (chief gunnery officer, 3 petty officiers, one per weapon type, and the 3 gunners) but only the gunners need to be in the turret if you assume it must be maned localy.
Leaving aside Mike's point that ships of 1,000 and under get crews in accordance with LBB2 rules, this is not how I read the HG crew rules.
The engineering section gets one crew member per 100 tons of drives, which must include a chief engineer, a second engineer, and several petty officers: 10% officers and 20% petty officers overall (I take the view that the chief engineer must ALWAYS be an officer; but that on a ship with less than 2,000 tons of drives the second engineer may be a petty officer, so the irreducible officer requirement in this section is 1, not 2.
Gunnery, similarly, requires a chief gunnery officer and at least one petty officer for each type of weapon aboard, but again I have always assumed that these are drawn from AMONG the total crew requirement of the weapons mix (1 per 100 tons of spinal mount; 2 per bay weapon; 1 per battery of turrets and 4 per screen) and not in addition to it.
I have tried to check these assumptions by reverse-engineering the smaller >1,000 ton designs in
Fighting Ships ... but this doesn't work. I always arrive at an irreducible minimum of 10 officers (7 in the command section, and one each in the engineering, gunnery and service sections) and yet the
Midu Agashaam is said to have a crew requirement of 6 officers and 27 ratings; whilst the
P. F. Sloan apparently gets by with 8 officers and 32 ratings, and the jump ship at page 22 (I never could figure why this appeared in
Fighting Ships!!!) has no gunnery section to test on - and still manages to be slightly light in officers, with only 8 of them.
The
Kinunir is the only one which appears to meet the HG minimum officer standard - but I believe it was originally designed according to a slightly different rule set in any event.