Hi Alan and Welcome to PSG
PS CC will always open with the last tool that you selected before exiting! so if you close PS with the Crop Tool selected it will open with that tool, if on the other hand you have another tool selected before exiting and it's still opening with the Crop Tool.
2 things you could try
Reset Tools
Failing that you could try resetting PS preferences, depending on the version you have you can either
Or the old school way
To restore preferences quickly using a keyboard shortcut: Press and hold Alt+Control+Shift (Windows) or Option+Command+Shift (Mac OS) as you start Photoshop. You are prompted to delete the current settings. The new preferences files are created the next time you start Photoshop.