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Did it say you authorize them to deduct the payment from your pay?
If you did not authorize them to make the deduction from pay, according to the FLSA they cannot do so and you can file a complaint with the US Department of Labor for that.
As far as the charging you for the damage, if they did not prove you did the damage, then you have a right to dispute that with them as well and could sue in small claims to recover the money they have taken from you, but you will have to provide the proof you did not do the damage they are claiming.