Almost all interviewers will ask you at the end of the interview whether you have any questions of your own. They say this out of courtesy more than anything else. At this point they are not expecting you to say or demonstrate anything that may change their mind about you.
By now you may have a feeling about how the interview has gone. If you think it has gone badly or you can't tell, the questions you ask may well rescue the situation. If you think it has gone well and the job is just about yours, be careful not to ask too many questions for fear of spoiling what seems to be a positive decision in your favour.
If they do not ask you if you have any questions, don't be offended. They may have forgotten this step or are inexperienced interviewers. Politely ask them if you could ask a few questions of your own. Just be sure it seems as if they have run out of questions and are looking for a way to end the interview. If they make excuses about why they didn't have time for your questions, then this is not a good sign. They have already made up their minds about you. It may be a positive decision, but don't count on it. Unfortunately it is difficult to do anything at this stage to change their minds. Proceed to end the interview politely and then hope for the best. Don't be tempted to continue the interview as you are leaving the building, this negative behaviour is unprofessional.