There appears nothing in the records related to his service with the 4th State Troops.

Civil War Diary of Richard Perry Harrison

“JULY 4TH, 1861. LEFT HOME JULY 4TH, 1861 FOR CAMP WALKER IN BENTON COUNTY, ARKANSAS. ARRIVED THERE ON THE SECOND DAY – FOUND A VERY PLEASANT CAMP SITUATED IN A LARGE PRAIRIE ON A MOUND ONE MILE FROM WOOD AND WATER. REMAINED THERE THREE WEEKS AND TAKEN UP A LINE OF MARCH FOR MISSOURI. . . . ABOUT THE 24TH [August] WE HAD A VERY NICE CAMP. COL HINDMAN MADE US A SPEECH TRYING TO GET US TO GO INTO THE CONFEDERATE SERVICE BUT WE ALL HAD HOME IN OUR HEADS TOO MUCH TO GO IN LONGER . . . . CLEANED OUR GUNS TURNED THEM OVER AND WERE DISBANDED ON THE 28TH . . . “

“ . . . I WISH SEVERAL OTHER BOYS GO JOIN CAPT PETTIGREW’S COMPANY [Co. K, 34th Ark.]. AUGUST 5TH, 1862 – SWORN IN TODAY FOR THREE YEARS OR THE WAR.”

“ . . . DEC 15TH [1863]– ORDERS COME TO REGT”L HEADQUARTERS FOR 5 OF US BOYS TO BE TRANSFERRED TO ENGINEER TROOPS. THE COL BURNT THE ORDER UP WHEN IT FIRST CAME & I WROTE TO GEN”L HOMLES ABOUT IT & HE SENT ANOTHER ORDER FOR US & SO GIP & I REPORTED ON THE 21ST DEC. – FELT VERY LONELY A FEW DAYS BUT FOUND THE BOYS & FORMED ACQUAINTANCES SO WE BECAME RECONCILED. . . .”

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At the breaking out of the Civil War he enlisted with the State troops and served three months in that command, when he was discharged and returned home, but later he enlisted in the regular army and served until the end of the war as a gallant Confederate soldier, having participated in the battle of Prairie Grove.

Obituary for Richard Perry Harrison
The Prairie Grove Herald
Thursday, June 8, 1911
https://familysearch.org/photos/stories/18085588

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Richard Perry Harrison
Birth: Oct. 12, 1843
Death: Jun. 2, 1911
Confederate Soldier
Co. K, 34th Arkansas Infantry the 4th CSA Engineering Battalion
Find A Grave Memorial# 41166974

See also: https://www.google.com/#q=Confederate+soldier+Richard+Perry+Harrison

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Richard P. Harrison, Private, Company K, 34th Arkansas Infantry, enlisted August 5, 1862 at Fayetteville by J. R. Pelligrew for 3 years [see diary], selected for Engr. Troops September 30, 1863, had not reported as of December 7, 1863, ** no further records

** see personal papers of A. C. Dickinson Capt. Engr. Troops

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Arkansas
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R. P. Harrison, Private, Capt. Dickinson’s Company, Engineer Troops,* transferred in effective November 1, 1863, no other records

* This company was known at various times as Captain Dickinson’s Company, Engineer Troops; Lieutenant Haney’s Company Engineer Troops; Company C, 1st Battalion Enginner Troops, and Company __, 4th Regiment Engineer Troops, C. S. A.

Compiled Service Records of Confederate Soldiers Who Served in Organizations Raised Directly by the Confederate Government.