I get paid hourly 20 dollars an hour. In 1 week I earned roughly $1025.00. However for some reason my company paid be twice in one week so I saw 1025.00*2 hit my bank. This obviously was in error and I want to pay them back; BUT a significant portion of the over-payment pay was taxed. It took roughly ~200.00 from the second payment made to me. So my question is; I should only be obligated to pay back the net over-payment not the actual 1025.00 correct? I never actually received 1025.00 in my bank, I received roughly ~800.00 of the over-payment of 1025.00. So isn't it fair that I only pay back the 800.00?
I can only speak for England and Wales, but I would expect other jurisdictions to be the same:
You are correct: you should only repay the excess cash that you received. Sorting out other deductions is your employer's problem.
This will be more complicated if this was the last payment in the tax year; speak to your local tax collection office. You might have to file taxes for the year.
Note that you don't actually need to volunteer the money back at all - you can just wait for your employer to ask for it back. (In fact, they may prefer to deduct the excess from your next paycheck(s).)
In practise (rather than as a legal question), I would talk to your payroll/HR department and ask them the best way to handle this.