Is the govt's Lisbon study legal?

The govt survey into why Lisbon didn't pass is out. I haven't yet tried to find the original and I wonder what questions were on the survey. I assume it was along the lines of

If you voted "no", was it because you thought Lisbon would bring a) abortion, b) EU army, c) corporation tax harmonisation?

The point being to uncover why "no" voters voted that way.

There could equally have been a survey that went along these lines

If you voted "yes", was it because you thought Lisbon a) would help fight climate change b) necessary for Croatia's entry to the EU c) would give national parliaments to ability to stop bad EU laws?

but no such survey exists.

Is it legal for this government to spend public money on a survey whose sole purpose is to help turn "no" voters into "yes" voters without also spending or providing money for a similar survey to investigate the misunderstandings of "yes" voters and correct them.