If no part of the bonus relates to any of the one month of work that you did in CT in 2016 and since not CT withholding were taken out, then just don't file any CT nonresident return for 2017.
If the CT department of Revenue contacts you (which is unlikely), then provide them with your explanation and your employer's unwillingness to correct their error on your W-2.
Alternatively, you may feel more comfortable with actually filing a CT non-resident state return for 2017 and report ($0) for the income. You must mail in this nonresident state income tax return (cannot efile a $0 state return) and include your state W-2 information. You will want to include an explanatory statement (a .pdf attachment) with your return stating your situation (that your employer incorrectly allocated a portion of your bonus income to CT and was not willing to correct the error).
This way you have proof that you actually did submit a CT nonresident state income tax return (mail certified) so as to avoid the CT DoR saying you had CT income but did not file.
