This depends on which theme you are using for your admin theme. If you are using a custom theme for the admin theme, you can add CSS in that custom theme. Otherwise, this is possible in a custom module via hook_css_alter().
Can you provide more information?
- Are you using a contributed theme or sub-theme as the admin theme?
- Which version of Drupal are you using?
- Does the CSS only need to be loaded on the user edit page? What are you trying to change on the user edit page?
I highly recommend reviewing the Drupal documentation on theming: https://www.drupal.org/node/341246
Here are some similar questions:
How to Override CSS for a core module?
How to override some admin theme CSS rules?
Good example solution: http://purewebmedia.biz/article/2014/04/23/adding-your-own-css-admin-theme