An Etymological Dictionary of the German Language/Schuld
Schuld, f., ‘debt, crime, guilt,’ from MidHG. schult (d) and schulde. OHG. sculd, sculda, f., ‘obligation, debt, culpability, sin’; comp. OSax. sculd, f., ‘debt, culpability, sin’; AS. sčyld, ‘guilt, sin.’ An old verbal abstract from the root skal, which appears also in Lith. skolà, ‘guilt,’ skìlti, ‘to get into debt,’ and skelěti, ‘to be indebted,’ as well as in Pruss. skallisnan, ‘duty’; Lat. scelus does not appear to be connected with it.