13A-11-30 defines Eavesdropping as interfereing with the Private Communication of others.
It can not be said, then, atleast in my opinion, that one can Eavesdrop one Himself.
If the Officer of Law interacts with you, in a non-Private Place, i.e. a Public Place, I would think that you would be within your Rights to Record that Conversation.
It is similiar to the Media, in essence.
As long as the News comes to Media, it is Legal.
Likewise, and in similiar fashion, as long as the Officer comes to you, presumably, it would be Legal as well.
I will look furhter into Alabama Code 1975, to see if I can locate any SunshineLawsthatpertain to moderntechnologies.