You certainly can file a lawsuit, but there are challenges you will face in suing the city in this case:1) The city would only potentially be liable, or responsible to pay, if you can show that they knew that the light was out--i.e. that someone had phoned it in or otherwise provided notice of the light being non-functional. They are not responsible if no one told them it was out, since in that case, they had no reason to fix it; i.e. they did nothing wrong in not fixing it.Furthermore, even if someone had warned them the light was out, it takes at least some time to get an officer on the scene to direct traffic (pending repairs); if the warning of the light being down came in just before the accident, they again would not be at fault, because they would not have had a chance to do anything.2)  Even if the city was at fault to some degree, you'd also have to show that you were driving carefully at the time--that you were looking to see if any cars were coming (traffic light or not, you always have to check the intersection, because some drivers go through red lights), were driving at a safe and appropriate speed, etc. If you were at fault, too, then even if the city was also at fault in not fixing the light (or having officers there to direct traffic) within a reasonable time frame, your own fault can reduce or even negate the amount of compensation you would otherwise get.Ideally, sue the city *and* the other drivers, to increase the likelihood that someone will be found to have been negligent or careless and therefore liable for your car damage and/or injuries.