We have lots of Laburnhams in our garden, I have cut out all the dead branches and they have survived ok. I expect that you could cut the overhanging branches off that you need to. We've trimmed a few of them that overhang the public path by our garden without them dying.

I think it is a case of trying not to let the tree become unbalanced and all the weight of it pulling over to one side. I'll try to post some pics of ours.

We have a very mature Laburnum that grows very upright. It has been cut with the extended pruner several times over the years......then it just goes merrily on growing and flowering well.

if you cut branches of there best done wear they join onto the trunk or bigger branch . to save taring underneath put a saw mark underneath about 6" from the trunk/bigger branch . then about a foot away cut your branch of . this will leave a little stump that you cut of as close to the trunk etc as you can for good healing and to save die back . not relevent if there just thin branches .any branches rubbing on another are worth taking out and as crv1963 sais keep it balanced . for what its worth you dont have to cut all or any branches of hanging over the nieghbers but it would be nieghberly to ask if there a problem or how much they want taken of as bye law they can cut of any branches hanging over there property and have to offer them back to you but its better being friendly and you dont know how well they will cut it or not as the case may be .

Recommended time to prune these is late summer, according to my book, but I used to cut mine back every year after it flowered, pruning back all the flowered shoots, mostly to keep it small and also to prevent seed falling. I'd leave any major pruning till later on though.