The rule of thumb is you should wait til you can form a ball with it that easily crumbles. If it's unadulterated clay i would wait at least a couple days for it to dry out. We are to get more rain today and saturday, and if i were you i wouldn't plant til tues or weds, after i checked the soil. That generality is more of an admonition not to till the soil when it's too wet- it messes up the structure- but i wouldn't plant either, because your plants could rot. Now, if the soil's amended, you'll find it becomes crumbly much sooner- even right after a rain sometimes. In that case, go ahead.

Also be aware that we are not past the 'frost free' date yet. I'm not sure what your plants are, but if they are tender, I would not plant them yet. You could set them out in the rain to get adjusted to the cooler (than in the house) weather.
Nancy