City officials are trying to charge me for an accident that was not my fault, a canine unit gave no warning and ran into my car just as I cleared the green light, totaled my car , with me and my underage child inside.

Was there an accident report ?

Who took the report ?

What does the report say you did ?

We're you ticketed ?

What does your insurance company have to say ?

Regardless of who was at fault, being on total disability and having a child in the car have no bearing in terms of protecting you from charges.
Sounds like you need a lawyer. Not just to fight the charge, but also in case someone decides your disability is affecting your ability to drive.

There is nothing preventing you from being sued. Your financial status may prevent anyone from collecting on the suit.

Where? I'm a liability investigator in NY. Anyone can pretty basically sue anyone for anything.

Collecting is another matter.

Maybe you are judgment proof. Maybe you are not.

But, yes, you can be sued regardless of what the accident report, witnesses and/or common sense indicate. Disability does not make you "sue proof."

Your title indicates "sue." Your thread seems to indicate "charged." Is it one or the other or both?

I am sure the other vechile has another side to the story, was the other unit running with lights and siren on ? Do they claim you ran the light "red" and they had the green,

But yes of course they may sue you, if you are found at fault, just let your insurance pay for the damages ? You have insurance ?
If you have no insurance and ordered to pay and do not pay, your drivers license can even be suspended till you pay or set up payment plan

If you are subjected to a civil suit, notify your insurance company. They will take care of it.