The issuing title agent, attorney or title underwriter is responsible for sending policies to the lender and the buyer. You should have a copy of the title insurance commitment in your hands before you close. Whoever issued the commitment, will issue the policy. Sixty days is a reasonable period to wait after closing without getting worried. After sixty days, make inquiries.
Some attorneys and title agents have bad habits. Some never issue policies. What crooks!
BTW - If you are trying to determine whether the title insurer you are working with is a good guy or a bad guy, ask about the title commitment and when you will receive a copy. The answer to that question is very revealing. It will separate the knowledgeable and dependable from those who are neither.