I was driving on a two lane street, I was behind a truck, he put his right hand signal,proceeded making a right hand turn, I proceeded driving by the time I was in the intersection, I was hit by the truck on my passenger side, he decided to make a left hand turn and damage my car, who's fault is this

You don't sue anyone. You report this to your insurance company and let them take over. If a lawsuit is necessary, your insurance company will handle it after trying to negotiate with the other driver's insurance company.

Therefore, please report this to your auto insurance agent who will make sure a file is started and a claims adjuster assigned. The adjuster will gather together all the "facts of the accident" and will be in regular communication with you.

If you can prove that he signaled right and started to move right, then fault would probably be his. But your saying the police report said something different?

As Wondergirl said, why are you looking to sue anyone? You report it to your insurer and let then handle it.

I'm a liability investigator in NY - too many unanswered questions here to even venture an opinion.

For example - where was OP's car struck? It's two lanes (and in legal speak that's two lanes total, one in each direction) or two lanes in each direction?

Yes, the only way it makes any sense is if there were four lanes, two one way and two the other. OP was in the center lane when the truck turned into OP's vehicle.

Because if there was indeed only one lane either way, I can't see how the truck could have collided with OP's passenger side. Was there an additonal right-turn ramp from which the truck driver suddenly turned left?

The big question here is how OP managed to be abrest of the truck. Another possibility, I suppose, is that OP was in the oncoming lane for some reason, and in the intersection, which is illegal and therefore proof of OP's contributory negligence.

I see this (if "this" is what we're talking about) all the time - #1 car signals a right (or sometimes a left) on a one-lane in each direction road. #2 car (behind the turning car) moves over/out to pass, often over the center line, around the turning car, not waiting for the car to turn. Car #1 doesn't turn OR turns in the other direction and - bang - into car #2.

My neighbor signaled a left-hand turn into her driveway, other driver swore she signaled a right and went to pass her on the left on a two-lane (total) road and they collided.

Unfortunately for the passing car I was standing out in front talking to the UPS driver and we both saw the entire accident.