I know what you're referring to but I'm not recalling where it is either. I'm not even certain it's in CT. Which probably isn't much help
My take for what it's worth...
First: In My Traveller Universe the Starport is extraterritorial to the generated local law level. This is not to say the Starport is lawless and everyone walks around with WMD's, rather that simple possession is not an enforced issue. Walk around with a laser or assault weapon at the ready on your shoulder though and you will draw attention from the local IMPs (Imperial Marine Police), and they are in BD (you aren't) with better weapons. So my "advisory" Starport LL is 5. No one will bat an eye at that.
Try to cross the extrality line though and you are subject to the local law level in both directions. So no contraband is permitted in either direction and people are screened for outstanding warrants.
That said I seem to recall what you're looking for stated the Starport LL is 3 and ignores ship's weapons, though as I said I don't recall the source. It seems to me that LL 2 would be more in keeping with the presumed responsible PC armament meme; ruling out only poisons, explosives, and undetectable weapons.
Per CT, Starport LL is implied to be equal to local LL, imo.
Second: I tend to make my world TL minimum based on the Starport quality. It's the locals that build and maintain the Starport (though it is run by Imperial agents) as one part of the requirements for full membership in the Imperium (as the step up from a Client State). In MTU Class A requires minimum TL9, Class B requires minimum TL7, Class C requires minimum TL5. Class D and lower require no minimum TL (though I might have rated Class D at TL3 minimum at one time).
Per CT Starport TL is implied to be equal to local TL, even where such a TL won't support the stated Starport services, which is a bit of a conundrum. Presumably the listed Starport services trump local TL so even at that TL5* world with a Class A Starport you can still build a Starship. Maybe with many imported components.
* the lowest possible for a Class A Starport world, on average you'll meet or exceed the TL9 minimum most of the time, so again it's a bit of a moot issue, most of the time