As replies to your question are, to date, limited to the one then I'll add a couple of observations.

To me it comes across as a mish-mash of uncertainty, incapability and less than ideal circumstances.

The area in which you all park sounds like it's poorly organised, maintained and policed.

But you know that.

But despite knowing that you haven't gained mastery of maneuvering your vehicles in confined spaces and can't judge, with certainty, where your vehicle's extremities are. Admittedly not so easy if it's, say, dark and wet and the car windows are misting up and you don't have reversing sensors fitted (and working).

You sound fairly relaxed that the underside of the car is prone to damage by the " mound" ... which, to me, is a strange thing.

Maybe you lack experience ... it sounds that way...coz, generally speaking an experienced driver knows when he's backed into another car or a low post or suchlike and would likely be able to differentiate between that sort of collision and driving over a raised obstruction that scraped the underside.

If your car is 13 years old and is parked where it's parked it's a mystery to me that your rear bumper has no scratches on it ... which is what you've said. Further more if you back into a flat panel (such as a door or wing) with thecorner of a bumper then the panel is likely to come off a lot worse than the corner of your bumper - so, to me, it sounds possible to have caused a smallish dent in your neighbour's car without sustaining much of a mark (at least enough of a mark to stand out from all the other marks ... and I simply don't believe that it doesn't have a few marks on it already.

To summarise then ... if your parking situation where you live is as haphazard as it sounds, and if your revesring skills aren't honed to perfection (which, to me it sounds like) and given that you're honest but uncertain what to do, then, clearly, you have no option other than to put all these circumstances to your neighbour in the hope that he/she is as honest as you (which they may well be) and you may well find they know about the dent already and you have a clear conscience - OR they say the dent wasn't there and you then have to come to an arrangement between yourselves.

The fact of the matter is... you suspect you may have caused damage to another vehicle in a public place and to neglect to make it known to the owner could come back to bite you in coming days (or possibly weeks). Furthermore you do, actually, have an obligation to inform your insurers because an incident is suspected and they ask (demand) to be told of any occurrence which may influence their assessment of risk. Even if your car was hit whilst stationary and unattended, you still have an obligation to inform them. Having said that the likelihood is that insurers need not be involved (which, in itself will save you hundreds of pounds coz even if they didn't pay a penny to anyone they may well up your premium next year for all the reasons that we all know).

But, the ball's in your court and you'll do what you or your conscience tells you what to do.

In the meantime get reversing sensors fitted and up your reversing skills.

If you can look at the face in the mirror and tell it in absolute honesty that you don't believe you hit that other car because you neither heard nor felt any impact that might suggest you DID hit it, and nor were you at any point close enough to have done so, then don't go knocking on doors and admitting to something you might not have done.

If, on the other hand you DO believe you might have hit that other car, and simply want endorsement of your decision not to cough to the blame because you can't make that decision on your own without feeling guilty, you've come to the wrong place.

If any of that sounds harsh, I've been there myself so I know how it feels.