At first glance Rising Star Games, company behind porting Deadly Premonition, didn't spend a lot of time on porting this game. There are zero graphical options, resolution is fixed on 720p and key binding can be done only via launcher that happily ignores some keys (alt, caps lock..). You can set mouse sensitivity, but beware of strong negative acceleration.
There is still hope as PC modding scene will probably fix many of its shortcomings. Durante already is busy with new version of DPfix - a custom d3d9.dll file, that modifies the game's rendering and lifts resolution restrictions.
In its current form the fix is far from perfect - in game map is rendered outside of its frame and some effects are not where they should be. However as a first aid it works fairly well so head up to Durante's website and get yourself a copy.
Installation is pretty easy - just unzip archive to the game's install folder (\Steam\steamapps\common\Deadly Premonition The Director's Cut\), then open DPfix.ini in text editor and set your desired resolution.
Update: Durante released new version of DPfix - 0.3 beta which fixes a lot of bugs:
- Fixed normal mapping/lighting of many surfaces in the game (this is a big one)
- Fixed minimap location
- Added windowed mode (in addition to fullscreen and borderless windowed fullscreen modes), since it was requested
There is one remaining issue with second camera perspective, so expect another release soon.