Some agencies use the same polygraph examiner and will accept a prior test given by that examiner, as long as it falls within a specified time frame.  Other agencies require a separate test and don’t care if you’ve taken other polygraphs.   

The only way to know for sure is to check with the Border Patrol and see what their policy is.  Most likely they will send you to whichever examiner they use and they won’t be concerned about prior polygraphs.  Good luck.

The Border Patrol is a federal job and they have their own process of conducting the background investigation.  That I know of they currently reserve the right to polygraph applicants, however, they do not polygraph all applicants and probably only do so to those that they feel has questionable issues that arose from the background investigation.

Failing your polygraph with the other police department is more than likely going to have no effect on the process with them.  I really wouldn't worry about it so long as you have nothing in your past that you are attempting to hide.  Just be honest with the investigator if he asks about it.

my husband won't try to apply because he smoke pot. he stop smoked a while back. he a good man 
pay the bills no crimes not even a parking ticket. should he apply?

dam even obama smoke at one time. please need an answer thanks