Hello, I just started on LSPDFR 4.0 Too.
I suspect the cause to be an overload of plugins on startup. It's happening to me at the moment.
I have Stop The Ped, Ultimate Backup, Smart Radio and a few others installed. The crash usually occurred when the police smart radio set up for the first time.
My suggestion is not get too many plugins yet. Try LSPDFR From stock and then work your way up one by one.