I accepted a job offer, received a start date, and all the other details of the job. I received an email from a company that does background checks and one of the questions is if they can contact my current employer. I don't start the new job for a couple of months, is it fine to say "No" to contacting my current employer? I just want to make sure everything passes and the new job is 100% secured.
Will it look bad on the background check if I select "No"? I want to keep working at my current job as the new job doesn't start for a few months. I feel like it might look bad if my current employer knew that I'm searching for other opportunities.
Any advice would be appreciated! Thank you.