You can install any (almost) 700c, or xx-622 tire where the first two numbers are the width, ie. yours are 38-622. There are practical limits, based on the actual rim width, which based on the existing 38mm tire probably isn't all that narrow.

Below is a chart showing rough guidelines for mixing tire and rim widths. Note that the rim dimension is the inside width which is 3-4mm narrower than outside width. Without knowing your exact rim,I would guess that you could very safely go to 28mm tires, possibly narrower.



BTW- there's plenty of debate about whether narrower tires are faster, or best tire width and pressure based on your weight, and I'm not going there except to suggest that you'll get measurable improvement by changing to slicks, then can get some (maybe) with a narrower or higher pressure tire.