Norm has some good feedback for you. Here are my thoughts ...
One, whatever you do, DON'T just divert water onto your neighbors lot because in most municipalities, it's illegal to do so. In other words, he can sue you if you 'alter' the 'natural flow' of water from your lot onto his. HOWEVER, you might be able to get away w/that if the 2 of you work out an agreement. If you do then the law will stay away.
Two, I don't know of a Municipality that allows a Homeowner to divert storm runoff into the Public Sewer. This may be semantics but you CAN divert storm runoff to a Storm Sewer. Storm Sewers vs. Public Sewers (as we've come to know them) are 2 different animals. In fact, in my municipality it's ILLEGAL to drain my Condensation Pump water into the Public Sewer! It has to go directly outside or into my sump pump. (The latter 2 drain outside anyways ...)
Now, where does all this leave you??? If you and your neighbor can't work something out, then you're left with 'collecting' the water and eventually draining it to the street. Assuming your water table isn't that high AND you have adequate sloping, you can build a dry well and run a pipe to the street (or to some other place that WON'T cause you or anyone a water problem.) Be sure to line your well with filter fabric BEFORE you fill it with gravel, and have enough fabric to COVER the top of the stone. Do compact the gravel at 3" intervals because if you don't, then over time it will settle and you'll have a 'depression'. Fill with gravel to withing 4-6" of the top, and cover with fabric. Then cut a piece of pipe about 6" long and put a 'drain vent' on one end, and stick the other end in a cut out hole in the top of the fabric. Wrap the pipe in fabric too. Then, with the pipe standing up, fill around it with dirt to the top of the vented end of the pipe. (The vented end should be 'set' at ground level ...) Then, plant grass seed or whatever. Get a leg-piece of nylon hoserie from a lady and 'slide a leg' over the vent pipe, and put the vent cap on. This way, if there's any 'debris' that drains towards the vent pipe, the debris is kept OUT of the well. Be sure to check the nylon a couple times a year to see if any holes are in it. Get new nylon if there are. (If the pipe becomes plugged, next thing you know, you'll be asking us why your drywell isn't working ...)
Good luck! My best to ya and hope this helps.
Jay J -Moderator
PS: E-mail me directly if you have any ?'s or post back here with them ...