Probably not, for at least two reasons.
First, your damages are an integral part of any personal injury lawsuit. Monetize your damages - what is a twisted ankle worth? A hundred bucks? A few hundred, at most? No smart lawyer will put time and effort into your claim when all he or she stands to gain is 1/3 of a hundred bucks.
Second, a broken sidewalk is likely an 'open and obvious' hazard. While businesses have a duty to keep their property in a reasonably safe condition, some hazards, perhaps like a broken sidewalk, are deemed to be so 'open and obvious' that a person encountering the hazard is expected to use caution and avoid the hazard.
If you damages turn out to be more extensive - for example, if you tore ligaments and tendons in your ankle, or broke your wrist in the fall, it would be advisable to consult with a local personal injury attorney to explore your options. But based on your injuries as described, its not worth your time or the time of an attorney.
Disclaimer: This does not constitute legal advice. No attorney-client relationship has been formed through this answer.
Unless the broken sidewalk was not obvious and unless your damages [medical expenses, lost wages, etc.] are substantial. No. Based on your description , you are partialy negligent at least for not acting as a reasonablle person aware of your surroundngs. Even if you overcome that hurdle, the descrition of damages is surely within small claims court where you cannot have an attorney.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.
If you want to pursue a personal injury claim against the store for negligently causing your injury, then the answer is yes/probably. However, premises liability cases (i.e. slip/trip and fall) are extremely hard and time consuming. If your injuries are not pretty serious, you will probably have trouble finding a lawyer willing to spend time trying to help you collect on the case. In order to do so, you have to prove your injury was their fault, not yours. And the insurance company will defend the case first denying that they were at fault at all, and secondly claim that even if the concrete was broken up, it was "open and obvious" and that your injury is your own falut for not looking where you were going. These are very difficult cases to collect on and you have to have an experienced PREMISES LIABILITY lawyer to know what evidence to get and how to present the claim. You will need good color photographs of the EXACT area where you fell. These photographs should also have measurement (i.e. with a tape measure) showing how big the "defective" concrete is. Ohio has a 2 inch rule that says if the "defect" is LESS THAN 2 inches, you lose! Thus, you should go measure the area carefully to see whether or not there is MORE THAN a 2 inch difference in the concrete where you fell. If not, you essentially have no case. If it is more than 2 inches, that is just the start of your ablity to bring a claim. You should also get good color photographs of your injured leg. The Statute of Limitations (time to settle or file a lawsuit) is two (2) years. Good luck!
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