HI,i have the same problem with my UT61E. If somebody have the same problem here is how i "resolved":
I resolved the problem removing the resistor vr1, I applied bigger and bigger resistor and then I removed definitely.
I think that the problem is somethig with the microcontroller.
I removed the resistance VR1 but the resistance between point VR and ground is aproximatly 100 kohm.
So without the resistance VR1 the lecture of the multimeter is passed fom -0.420V to -0.04V.
I'm satisfy with this result but know it's not a long term fix.
Now i think that UT61E is a shitty multimeter.
![Uni-T UT61E shows negative DC voltage w/o probes](https://www.eevblog.com/forum/index.php?action=dlattach;topic=208872.0;attach=1220004;image)