No, there is not.
Generally, “checks” (ability checks, skill checks, initiative checks) do not have critical effects, and there are some very good reasons for that (5% failure rate is inappropriate for most of them, plus in many cases what would happen on “auto-success” is very unclear: take Jump for example).
Natural-1s on saving throws, attack rolls, some of the opposed rolls (grappling, etc), is auto-failure. Natural-20s on the same rolls, and so on, is auto-success. In attacks’ case, there is also a chance of a critical hit on a natural-20 (or less for some weapons).
Generally speaking, expanding these rules to other sorts of checks is very ill-advised.