I agree with lateral line, any fish can carry desease, but, neon tetras often(but not always) show quite obvious signs of distress when they are feeling unwell like being constantly faded looking or not shoaling with the other neon tetras- when it comes down to it though, you should preferably quarentine fish for around 2weeks+ if you can when you buy them as this is one of the sure-fire ways of making sure new fish aern't bringing any new deseases into the aquarium.
The desease you really have to look out for when buying new fish is whitespot, as it is a very common and very infectious and devastating desease which is invisable to the human eye during many of its parasitic life cycle stages and infected fish may not show any symtoms of it for up to 2weeks depending on the tank conditions- most other deseases though become apparent within the first few days of infection, and thankfully many are not as infectious as whitespot.
Are you intending to buy new neons or concerned that any you might currently own are sick?