The standard of proof in civil cases is the "balance of probabilities". Conceptually, this means that if you can convince the court that the alleged event occurred with a 51% probability, then you should be able to succeed.
Family law cases are civil cases. However, because family law cases often concern the best interests of a child, the rules of evidence can be relaxed, for e.g., introducing the child's hearsay evidence - but that is a topic for a different post.
What does a court do when asked to consider whether a future harmful event to a child could happen in the future? To illustrate, consider whether the reasoning should be same in the following scenarios:
- Did the child abuse indeed occur in the past?
- What is the likelihood that the child abuse will occur again in the future?
- Was the child harmed by the parent not brushing her teeth yesterday?
- Will the child be harmed by the parent not brushing her teeth tomorrow?
- Was the child harmed by the parent breaking her arm yesterday?
- Will the child be harmed by the parent breaking her arm tomorrow?
S.H. v. British Columbia (Child, Family and Community Service), 2015 BCSC 230
The court considered these questions in the case of S.H. v. British Columbia (Child, Family and Community Service), 2015 BCSC 230. This case was a child protection proceeding. This sort of proceeding pits the state against the parent, instead of pitting one parent against the other. In this case, the trial judge had made a finding that the child was in need of protection against the mother, and the mother had then appealed the trial judge's decision. On appeal, the court clarified the standard of proof in the child protection context in relation to assessing the threat of future harm to a child.
The following passages from the leading case, B.S. v. British Columbia approving its previous decision in British Columbia (Superintendent of Family and Child Service) v. G.(C.), 1989 CanLII 2967 (BC CA),  22 R.F.L. (3d) 1 (B.C.C.A.), on the issue of threat of future harm to a child were highlighted in the appellant's materials, at paras 118 - 119:
- I do not have any doubt that the burden of proof in child protection cases rests on the person who asserts the need for protection. Nor do I have any doubt that the standard of proof is the standard in civil cases, namely, the standard usually called "the balance of probability". Sometimes, in applying that standard, the seriousness of the allegation being made is thought to require a higher and more particularized measure of confidence on the part of the decision maker that the balance of probabilities test has been met. But the test remains the same. The weight of the evidence must show that it is more probable than not that the assertion being made is correct.
- When the assertion being made is about a past event then the actual occurrence of that event must be shown by the weight of the evidence to have been more probable than not. That is the case with past abuse, neglect, or harm to a child.
- But where the assertion being made is that there is a risk that an event will occur in the future, then it is the risk of the future event and not the future event itself that must be shown by the weight of the evidence to be more probable than not. That is the case with consideration of a threat of future harm.
- The result is that in considering past abuse and the degree of certainty that it has occurred will be more than is required in considering whether abuse will occur in the future. A ten percent risk of future abuse may meet the test of the risk being shown to exist on the balance of probabilities, whereas a ten percent assignment of the probability that the abuse has occurred in the past would not meet the balance of probabilities test.
- In assessing the risk of future harm, (which is called the threat of future harm in s.2), there is room for a variable assessment depending on the nature of the threatened harm which is in contemplation. A threat of harm through neglect of the child’s hygiene might well have to be much more probable in order to meet the balance of probabilities test than a threat of serious permanent injury through physical or sexual abuse. Generally speaking, a risk sufficient to meet the test might well be described as a risk that constitutes "a real possibility".
- [Emphasis in the original].
In the case at hand, the court clarified the above passages and confirmed that there is only one standard of proof, that of the "balance of probabilities". But, when considering the risk of future harm to a child as opposed to risk of harm, there may be different evidentiary considerations as stated in para 20:
-  I would not accede to this ground of appeal for two reasons. First, in my view the decision in B.S. v. British Columbia does not stand for the proposition that there is a different standard of proof in child protection cases involving the risk of future harm other than proof on a balance of probabilities. Rather, that case confirms that the standard of proof is the balance of probabilities, though there may be different evidentiary considerations when analyzing the risk of harm to a child from past events as opposed to future events.
In sum, it appears that there is a distinction to be drawn when considering the risk of future harm to a child versus risk of past harm to a child. It also appears that a threat of harm arising from a less serious risk might be considered differently than a threat of harm arising from a more serious risk.
Does the analysis above apply in a proceeding between parents?
In the case of N.N.K. v. S.F.L., 2014 BCPC 297 (CanLII), the court used the analysis above at para 77 and 78. However, it should be kept in mind that this was a provincial court proceeding.