This question has many variables, making it impossible to give a truly clear-cut answer. For starters, we will assume the term “co-parent” to refer to two parents who raise the child together, even though they are separated, divorced, or no longer living together (however, co-parenting can take various forms under court-imposed orders for sole custody, joint custody, shared custody, etc.).
And in terms of “personal business”, we will assume this means non-child-related information such as the child’s day-to-day activities, including school time and obligations, health care, sports and other extra-curricular activities, social connections, etc. These listed items may also be specifically covered by a court order for child custody/access, where a judge has required you to disclose certain child-related information to each other. In that case, you are certainly required to disclose that information as ordered. For access parents, there is also Ontario legislation in the form of the Children’s Law Reform Act that confirms that an access parent has the right to “make inquiries and to be given information as to the health, education and welfare of the child.”
But for matters not covered by court order or legislation, as a general rule a co-parent is not entitled to intrude into your non-child-related personal business, at least where it does not impact the best interests of the child.