I found 2 Partirick Connelly's who were naturalized in the Pennsylvania supreme court.

The first was naturalized October 10,1864; he had arrived in New York in 1837.
For a copy contact the Pennsylvania Archives in Harrisburg, Pennsylvania.
Record Group 33 Roll 806 Naturalization #5791

The second was naturalized on September 26, 1867; he had arrived in Philadelphia 1861.
For a copy contact the Pennsylvania Archives in Harrisburg, Pennsylvania.
Record Group 33 Roll 806 Naturalization #8441