On an onat perishah, relations are forbidden, and a bedikah is required to maintain your chezkat taharah (halachic presumption that you aren't niddah), or to find out if you have begun menstruating. Everything else (touching, hugging, kissing, passing objects, etc.) is okay, but it is a good idea to refrain from activity which could lead to relations.
After the onat perishah, if the bedikah was fine, a couple may resume all physical contact, including intercourse. If you suspect you are supposed to get your period that day, common sense would say you should refrain from relations, but there is no halachic obligation to do so. It is also fine, and in some circumstances prudent, to check yourself before having relations to make sure you haven't started bleeding. You can do this by wiping externally with toilet paper, not immediately after urinating, so that if you do find a stain it can be treated leniently and will not make you niddah.