My wife did some billing work for her brothers medical practice in Denver. The majority of the work was done on-line from California as we are California residents. She stayed with her brother for a total of about 45 days, listing his address on all payroll/w-4 Ect. Does she file as dual or part time resident for CO.?

You can probably get away with her NOT filing a Colorado tax return at all, given the short duration of her stay.

It is likely that any income earned would be exempt from Colorado taxation due to her personal exemption and the Colorado version of the standard deduction.