I cannot interact with menus from my controller because menus only accept the keyboard as an input.
What is curious is that pressing the directional pad or left joystick or the X button on the gamepad triggers a sound effect but it doesn't actually do anything.
Since you made the game playable with a controller, I think you also should bind controller's keys to interact with menus.
From the way you made the gameplay and from which buttons trigger sound effects in menus even if they don't do anything, I would say that the most appropriate binding to do is directional pad or left joystick for navigating in menus and X button to confirm.
Also, even with the keyboard, "continue" and "restart" from in-game menu don't work, meaning that once you pause the game, you can't resume it and have to quit it and launch it again, and "restart" from game over menu doesn't work either, I have to quit the game and launch it again in order to retry, which is boring.
And the fucking giant bats are unavoidable as they cross the screen at sonic speed and you can't do anything if you are on their path!
Please, remove them or make them some regular smaller, slower mobs who get along with the zombies, like they come out of trees when you come close to their tree and fly in circles around you trying to hit you until you are out of reach of their tree or something.
These flaws aside, I like the game. :-)