Picture what a dumpy level actually needs to do: when you centre the bubble, the telescope's line of sight must come out perfectly horizontal, whichever direction you point it.
For the vertical axis to stand truly vertical whenever the bubble is centred, the bubble tube's own axis has to sit at a right angle to that vertical axis. That is exactly what keeps the instrument level all around as you rotate it, so Statement (I), which says the bubble tube axis should be perpendicular to the vertical axis, matches the real design requirement.
Now think about the telescope's line of sight. If this line of sight were perpendicular to the bubble tube axis, then centring the bubble would point the telescope straight up or down instead of horizontally, making the instrument useless for levelling. The correct requirement is that the line of collimation must run parallel to the bubble tube axis, so centring the bubble automatically makes the line of sight horizontal. Statement (II) claims perpendicular where it should say parallel, so it is wrong.
Putting the two findings together, Statement (I) holds up and Statement (II) does not.
\[\boxed{\text{Option 3: Statement (I) correct, Statement (II) incorrect}}\]