Topload maytag washer partially fills by its self overnight or even a day or two may pass.

Warning! To avoid personal injury or even death, always disconnect your appliance from its power source--that is, unplug it or break the connection at the circuit breaker or fuse box--before you do any troubleshooting or repair work on your appliance. Also, because some components may have sharp edges, use caution while working on your appliance.
Your washer has a defective water inlet valve.
The link below is courtesy of. www.repairclinic.com,
They also provide repair parts, disassembly diagams and procedures.
http://www.repairclinic.com/SSPartDetail.aspx?s=b4a11i868761&PartID=868761
This may not be the exact part for your washer.
You will need the complete model number from the product ID tag which is affixed to your washer, to obtain the correct part.


TIP:
If it is convenient, it is advisable to turn your washer faucets off when not in use, to prevent accidental flooding