Can bd take kid across state lines?

Location: Colorado. My gf has a 4 year old and her and baby dad split over a year ago. There’s no custody agreement or anything through the courts so I’m wondering if he’s allowed to take her across state lines without mom’s permission? Google gives me mixed answers and my dad told me from experience with my mom that he had to get written permission even though they both had custody of us. He’s wanting to take 4yr old to Nebraska about 2 hours away. He doesn’t have a working vehicle and we know her well being would not be safe. Is there anything we can do if he goes against the permission?