How should you answer 'May you contact your employer' if you don't want your employer knowing you are looking for a job?

If I was you I would mark no and then explain to them why you answered it this way. Most employers will understand why you dont want your current employer to find out you are looking for employment elswhere.

A different perspectiveAs someone who evaluates applications and interviews and hires people I would unequivocally state that you should always answer yes. ing no to this question indicates you have something to hide. Any company looking at applicants already assumes the candidate does not want their current employer to know they are searching for a new job, and of course it will show on your application that you are currently employed by said company. If somebody does contact your current employer, it means you already have the job and they're following up by checking facts.