I will be happy to help you out.
How big was the puddle of oil?
Size of coin? Hand? a plate?
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You have a maytag/whirlpool. Your machine says maytag on the control, but was built by whirlpool. Your transmission on the top has a breather hole. When you tilted the machine back oil leaked out of this hole. I don't believe enough oil has leaked out to give you any problems. There is a lot of oil in those so this will not cause any heat or lube issues.
Some oil may have gotten on the clutch, but after a few loads this will be gone. I would do smaller loads the first few times you wash clothes with your machine. Other than that you should be good to go. I wouldn't worry about the oil other than the mess it has made on your floor. Maybe lay a couple paper towels under the machine for a week or so until the rest of the oil runs off. After that you won't have anymore leaks. This is not an uncommon issue. If enough leaked out I would recommend filling up the transmission, but only enough to cover your hand is not that much compared to the amount in the transmission.
If you have anymore questions please feel free ask.
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On this transmission there is not fill hole. The only way to fill with oil is to remove the cover of the transmission. There is bolt down the center of the agitator. Take out that bolt. Now tilt the machine back. There are 3 bolts that hold the trans. in. Four bolts will remove the transmission. You will have to take the motor and pump off also.
From there, you will have to remove the clutch from the top of the trans. This is help into place by one lock ring. Once that is out, there are about a dozen screws holding the cover down to the top of the gearbox. Take that off and fill it to the top.
After that, put the pieces back together. With a little patience and some room to work, this is a job you can do yourself. If you are not comfortable pulling the machine apart then I would leave it up to a technician. If you start to do this and get stuck. I will help you out the whole way through.(even over the weekend)
Let me know if you have anymore questions about this. Thanks Again for using JustAnswer.com!