It's true that when confidence intervals don't overlap, the difference between groups is statistically significant. However, when there is some overlap, the difference might still be significant.

Can 95 confidence intervals overlap and still be significant?

When 95% confidence intervals for the means of two independent populations don't overlap, there will indeed be a statistically significant difference between the means (at the 0.05 level of significance). However, the opposite is not necessarily true.

Can two confidence intervals overlap?

The short answer is: not always. If two statistics have non-overlapping confidence intervals, they are necessarily significantly different but if they have overlapping confidence intervals, it is not necessarily true that they are not significantly different. We can illustrate this with a simple example.