The ground should be moist when you plant your grass seed, so waiting until after rain is more effective than planting before. If the soil is damp, it is also easier to work with.
The best time to plant grass seed is in the autumn on a clear day right after rain. However, it should be early enough in the season that the ground hasn't frozen over.
Do not plant grass seed following a heavy rain, however. If the ground is muddy, it can be hard to work with. Too much water will make the grass seed rot.