This is a very targeted question. They could have just asked “What would you do if you saw someone cheating on the civil service exam,” but they want to see how you react to a more ambiguous field situation. The panel is looking for a few things when asking this question. They are trying to determine how you will react when you think you see something that is nefarious in nature. On the surface the question is probing you on how you will handle a situation when you see something happen that is illegal. However this is a chance to give the panel some insight into how you view people in general. Do you generally think the worst or best in people. This is going deeper into the question and giving the panel a better understanding of who you are. The key here is to not assume that your partner is stealing because you realize that this department vets all its candidates thoroughly and they hire the best of the best. Your approach should be to let your partner know that you saw them take the wallet but do it in a tactful, non-accusing way. This will give your partner the option to do the right thing and it allows you to think the best of your partner. Finally, you need to tell the panel that if your partner does not do the right thing and steals the wallet, you will utilize your chain of command and turn your partner in. The panel will not be able to write fast enough and score you high on this answer. You have taken this question up a level.
First of all, this is an awkward situation and I have to handle this sensitively. I would approach my partner and say, “wow good find”. “The homeowner will be very happy when they get their wallet back”. Can I be there when you return it I want to see the look on their face”. “The Chief will be proud that you went above and beyond on this one”. Now I present it this way because I see the good in people and I do not assume that my partner is stealing the wallet. I further understand this department has put all personnel through vigorous background checks and you hire the best of the best, so I have no reason to assume my partner would have such low character. However, I have to leave open the option that my partner is up to no good so I let them know that I saw them take the wallet but I do it in a non-accusing fashion. My partner now knows that I saw him take the wallet and I will be telling the chief about the incident. I have given my partner every opportunity to do the right thing. If they choose to do the wrong thing then I will utilize my chain of command to report the incident.