Dating a work colleague

I met this guy at the start of September we work in a school environment and we started chatting more two weeks in. We speak a lot like everyday and I see him at work too! We went to costa on the last day of term together just as friends, a week later he took me bowling and then went out for drinks where he told me he liked me and wanted to slowly become more than friends which I agreed too! We’re seeing each other now but we’re keeping it private and not telling work! Is there a contract or something we have to sign if we date someone at work?