Maybe. the problem is that your damages do not make it economical for you to hire an attorney. You need to send the City notice of your claim. Describe what happened: where, when (including hour of the day), and how. What your damages are: the total loss value, not the deductible. Tell it that it's negligent use of property caused your damages. Send your letter by certified mail, return receipt requested.
You need to send the notice asap. Time requirements for notice vary from city to city.
Talk to your insurance agent. Your insurer may want to pursue this claim and, if so, might collect your deductible for you. If not, it can tell you when you are free under your policy to work on recovering your deductible; but send the notice letter out now.