I found on P. Murphy in Kentucky units,

Patrick Murphy
Residence was not listed;
Enlisted on 11/16/1861 at Louisa, KY as a Private.
On 1/10/1862 he mustered into "A" Co. KY 22nd Infantry
He deserted on 11/17/1862 at Louisville, KY

Sources used by Historical Data Systems, Inc.:
- Report of the Adjutant General of the State of

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There are 26 Patrick Murphy’s in Yankee units from Massachusetts who survived the war. Do you have any other information which could narrow the search, say, residence in 1860, occupation, etc.?