If the legal definition of "statistically significant" is different from the statistical one, then it is very likely to be a deeply misleading one, and one that suggests the evidence is much stronger than it actually is. In this case, described in the OP, the question about statistical significance is clearly from someone that has no idea what it actually means, and the best approach is to see if the question can be posed in layman's terms avoiding statistical jargon, so it is clear what they really want to know. Dean's answer is a very good one. However, telling people that they are wrong sometimes goes down badly, but I would hope that judges and lawyers would have the good sense to allow themselves to be corrected by a domain expert when they are wrong.
I thought it might be useful to explain why this phrase is likely to be misunderstood - it is because statisticians (at least those performing null hypothesis statistical tests) and laypersons are likely to have fundamentally different ideas of what is meant by a probability.
The original definition of a probability in statistics was similar to the everyday meaning - it is a numerical indication of the relative plausibility of a proposition, e.g. there is a probability of 30% that it will rain today. However, there is a "subjective" element to this, as the plausibility may depend on your prior beliefs (or equivalently your state of knowledge). A new branch of statistics came about, called "frequentism" in the 20th century that aimed to eliminate this "subjective" element and have a purely objective means of performing inference. They did this by defining a probability only in terms of long-run frequencies. This is perfectly reasonable, but it does mean you cannot assign a probability to a particular event, only to populations of events. For instance, a frequentist fundamentally cannot tell you the probability of a particular DNA match being a false-positive - it either is a false-positive or it isn't - it doesn't have a non-trivial long run frequency, so you can't assign a probability to it. So what do we do? Instead of "probability" we speak of "confidence" (as in "confidence interval") or "significance" (as in "statistically significant"). I think originally, this was intended to highlight that it isn't a probability and avoid misinterpretations, but sadly this is not how it has turned out.
The key problem is that we normally want to ask a question about a particular case (e.g. this DNA match), but a frequentist statistician cannot answer that question, so they substitute an answer about some (often fictitious) population (e.g. on average over a large number of DNA tests of which this one is representative in some way that is most often left explicitly unspecified). The questioner hears this and interprets it as an old-fashioned (degree of plausibility) based answer about the specific case - because that is what they were expecting (not unreasonably).
So if there is a legal definition of "statistical significance", it is very likely based on this "degree of belief" definition of probability, and be a bad misinterpretation of what was actually meant by the person that conducts the test. This isn't particularly the fault of the legal profession, statisticians often shy away from explaining what things mean because the audience is often very hostile to it.
Bayesian statistics is likely to be a better match for the needs of the Law as it is based on the same basic definition of a probability that the layperson uses, and hence is less likely to be misinterpreted.
The way statistical hypothesis test should be used is as a minimal hurdle that prevents you from making a fool of yourself by getting carried away with your research hypothesis (the thing you want to be true). A statistically significant outcome just means you have stumbled over the hurdle somehow and you can still talk about your research hypothesis. If it wasn't significant, you should not talk about it as if it were true (yet). It really doesn't mean very much, and is most useful to your when non-significant.
