The best time to plant grass in Michigan is in the fall. This gives the seedlings time to root for the winter and then start the following growing season with an established root structure. You can also plant in the spring, but remember that weeds are actively growing, and heavy spring rains may cause wash-outs. Avoid planting in summer, if at all possible. If you must plant grass in the summer, mulch the area with peat moss to keep the seed from drying out and to keep weed seeds from establishing in your new grass.
Cool-season grasses grow in Michigan. A cool-season grass does most of its growing in the spring and early fall. Naturally, these times are also the best for planting grass. Don't define "early fall" by the fall equinox, which falls on either September 22nd or 23rd, depending on the year. Instead, think of late August and the first weeks of September as "early fall." Temperatures are beginning to fall and cool-season grasses are ready to grow again.
Weeds, however, are not growing at this time, which is why it's a perfect time of year to plant grass. The seedlings will be able to take root and flourish without any competition from weeds. Pests and disease are also less prevalent then. Don't plant grass too late in September, as the seedlings need time to take root for the winter.
All varieties of cool-season grasses are best planted in the fall, whether it's Kentucky Bluegrass, Fescue or a mix. If you must plant grass in the spring, do not use pre-emergent herbicides. You can plant grass in the spring when the ground is thawed and dry enough to be worked. If you expect March or April snows, it's best to wait until the threat of those has passed.