Is there a Legendrian Neighbourhood Theorem also for non-cooriented contact manifolds? Dear Daniele Sepe, first of all, thank for your attention to my question, and sorry for the delay in my comment; initially, some activities forced me to reduce my presence on the site, then, I forgot of you answer. Now, I do not know if, in the meanwhile, you went somewhere with the modified question. But I have found a 1998 paper by F. Loose which gives a positive answer exactly to that question after having chosen the graph of the $1$-jet of the zero section of $p:L|_N\to N$ as the normal form of contact manifolds on a neighborhood of a legendrian submanifold $N$.