It's not clear to me if you are a legal employee of the NY company, or if you are an employee of the CPEO and your services are contacted through the CPEO for the NY business. Is your contract with the NY business or the CPEO?
If you are a legal employee of the CPEO, the convenience of the employer rule does not apply. If you are an employee of the NY business, read on. (However, if you physically worked in NY state for any period of time, such as training or orientation, that is going to be considered NY-source income and you will file a non-resident NY return. This is part 3 below.)
Generally, you owe a resident income tax return to the state of your permanent residence, reporting and paying tax on all your world-wide income. In addition, you may owe a non-resident tax return if you have income that is considered "sourced" to another state. Most of the time, source is determined by where you physically lived or physically performed the work, regardless of where the company has its offices. But New York is one of 7 states that has the convenience of the employer rule.
Part 1:
The convenience of the employer rule does not apply if you never set foot in NY during the tax year. If that is true, you need only need to file a non-resident NY return if you had NY tax withholding. You would report zero NY-source income, zero tax owed, and claim a full refund of the withholding. You will file a Colorado return that reports all your world-wide income, and pays Colorado tax. Hopefully you had Colorado withholding.
If you physically worked inside New York for even one work day (such as orientation, meetings, training, etc.) then the convenience of the employer rule applies. The next step is determine if you worked in Colorado for your own convenience or for the convenience of the employer. You are working remotely for your own convenience if the company has an office for you and you could work there but choose not to. You are working remotely for the employer's convenience if they want to you work remotely (maybe you have duties that require you to be present in Colorado, or maybe they closed their NY offices and don't have room for you.)
Part 2:
If you are working remotely for your own convenience, you must file a NY non-resident return that reports your NY-source income and pays NY tax. You will file a Colorado resident return that reports all your worldwide income and pays Colorado tax; Colorado will give you a credit for tax you paid to New York.
Part 3:
If you are working remotely for your employers convenience, then your income is only considered NY-source for the days you physically lived or worked in NY, such as for training or meetings. Suppose you started the job on July 1 and had one week of training NY, then 1/26 of your wages would be NY-source (3.85%). You
you file a NY non-resident return that reports your NY-source income and pays NY tax. You will file a Colorado resident return that reports all your worldwide income and pays Colorado tax; Colorado will give you a credit for tax you paid to New York.
Lastly note that if you file a Colorado resident and an NY non-resident return, you must manually allocate your income to NY, Turbotax won't know how to do it for you. Interest, capital gains, prizes, and other income is sourced to where your permanent home was located when it was paid. Your only income that should be allocated to NY is part or all of your NY job income, depending on the circumstances.
