Is a county responislbe if it permits a septic drainfield, inspects it, and it is later found to encroah across a property line? DOes t

Typically the purpose of the county inspecting the drainfield is to determine that it meets health and safety standards, rather than to verify that it does not encroach on a neighbor's property.  You may have had to show proof of ownership of the property in your application for the construction permit, and the county may have verified your ownership, but that does not mean the county could determine that the drainfield would encroach on a neighbor's property.  Proof of encroachment would require a survey of the land with surveyor's stakes on the land showing the actual boundary line.  Unless the survey stakes were on the land, the county would have no real way of knowing that the drainfield was encroaching when they inspected the property, and even if they were there, the inspector would not have reason to pay much attention to them.  Finally, the government typically considers boundary disputes to be private matters between owners that have nothing to do with the government.  You have not indicated whether you are the one encroaching or whether you are being encroached on.  When you ask "what is the statute of limitations on encroachments," I think you are asking how long it takes for someone to establish a right to encroach either by adverse possession or prescriptive easement.  The time period on either of those used to be 5 years of open, notorious use (i.e., the other party was aware of the use but never gave its permission) but in 2006 the law on adverse possession was modified to make the period be 20 years and the new law created uncertainty as to whether it applied to both adverse possession and prescriptive easements.  So the period is either 5 or 20 years but it is necessary that the other party was aware of it without attempting to put a halt to it for that full period of time.