Court records?

[Kimberly Maher]

My Gr-Gr-Grandfather, Bror Carl Springert, Oct 12, 1850, Härnösand, Vasternorrland, was illegitimate. I have been told the only real way to find out his father, since he was not mentioned in the church records, is if there is a court case. His mother, Maria Brita Springert, lived in Skön until the time of his birth. Is there any way to see court records for either of those two districts for that time period?
 
Thanks.
 
Kimberly