Here is what I have on this man. He may be related to the soldier I have appended below:

CONNELLY, NEAL F. : C. S. Company C, 16th Arkansas Infantry Regiment Sgt/2Lt. Enlisted 7 Oct 1861 at Clarksville as 2nd Sergeant. Age at enlistment: 27. Elected 2nd Lieutenant 30 Oct 1861. Captured 8 Mar 1862 at Pea Ridge. Sent to military prison at Camp Chase, Ohio. Transferred to Johnson’s Island, Ohio 24 Apr 1862. Transferred to Alton, Illinois Jul 1862. Forwarded for exchange to Vicksburg, Mississippi 1 Sep 1862. Formal exchange dated 8 Nov 1862 although he had already rejoined regiment. Appointed assistant surgeon of the 7th Arkansas Cavalry Regiment 22 Aug 1864. Age listed as 30. Born 1835 in Tennessee. Age listed as 17 on 1850 Johnson County Census. Present at 1892 U.C.V. meeting at Clarksville. Filed Pension Application (#6054) 10 Aug 1905 from Johnson County. Died 1910 at Dardanelle, Pope Co., Arkansas Buried in Oakland Memorial Cemetery, Clarksville, Johnson County.

CONNELLY, WILLIAM H. : C. S. Company D, 62nd Arkansas Militia Pvt/Pvt.
Company L, 7th Arkansas Cavalry Regiment Pvt/Pvt. Enlisted 2 Sep 1863 at Clarksville. Born in Tennessee. Age listed as 39 on 1860 Johnson County Census. Filed Pension Application (#6029) 4 Aug 1904 from Johnson County. Buried in Oakland Memorial Cemetery, Clarksville, Johnson County.