The answer to this question probably depends on many issues including how long the sidewalk had been that way, whether there were any other trip incidents on it and whether the city was aware of the condition of the sidewalk. Additionally, there may be immunity issues since you would be making a claim against a government entity, and there may be a very short notice of claims period in which you must give the city notice if you intend to make a claim.
It is in your best interest to consult with an experience MI lawyer very soon.
Act quickly; consult with an attorney, file a notice of claim, take photos, get witness statements, retain an engineer, etc. Some or all may apply. Good luck.