What Does His Word Against Mine Mean And Would It Stand Up In A Court Of Law?

"His word against mine" means that he may (an usually is) saying something that is the direct opposite of what you say.
In a court of law, the judge will listen to both sides and make a ruling based upon his best judgment and experience.
The things that will best help your case will be witnesses and /or documents such as canceled checks to present to the judge in small claims court.

While under arrest  I was taken to the hospital in a knee high cast  hand cuffed a policemen said I kicked him and than massed me I did not kick him