Two houses, one driveway

[Randy E.]

I bought a house recently that will be a rental.  Prior to buying it, I noticed there was only driveway for this house and the one next to it.  I checked online and it appears the driveway is mostly on the other owner's property.  I bought the house anyway because the deal was too good.

Now, I've discovered a cement pad in the back yard that was covered with leaves and overgrown grass.  And I've looked at an old map of the house that shows a small structure in that spot that I'm guessing was a small detached garage.  Now, I'm wondering if the driveway was historically a shared driveway.

At the street, the driveway is 90% in the other yard, and 10% in my yard.  Looking at it in person, the driveway is only deep enough for one and a half cars and at that point it just merges into the grass of the yards.  Looking at the map provided by the city, I can clearly see the driveway continue all the way into the back yard.  As the driveway goes between the houses and into the back yards, it gradually moves more and more across the property line.  By the time the driveway (on the map) reaches the cement pad of the no-longer-there detached garage, the driveway is 100% on my property.  

My guess is it was historically a shared driveway, and each household veered off and parked in their separate back yards.  I'd like to figure out if there's a way to continue to use it as a shared drive and allow my tenants to park in the back yard.  I'd pay to lay gravel and such, and even for the neighbor's yard too.

Just trying to find out how to go about this.  I'd like to know where I stand legally before broaching it with the neighbor.  The neighbors are nice people (so far) but I'd like to find out my rights before asking them about it.

Ideas?