From a legal standpoint, no. However, while it makes no difference to the judge in Colorado which party files for divorce, filing first can have some personal advantages depending on your situation.
Every relationship is different, and more often than not both parties are well aware of an impending divorce. But if you are looking to take your spouse by surprise, being the one to officially file the divorce paperwork is certainly one way to do so. By filing first, you can line up your team of lawyers and advisers in advance and not be scrambling last minute to find representation. You have the advantage of mentally preparing and gearing yourself up for any upcoming battles with your spouse. You also get to be the one to set the timeframe for the proceeding and you will get to present your case first at trial.
Additionally, according to Forbes, filing first allows you to decide the jurisdiction that will govern your divorce. If, for example, you spend time equally at homes in Colorado and California or you and your spouse are separated and live in different states or counties, you can choose where to initiate the proceedings and which jurisdiction's laws will work better in your favor.
Conversely, there may be some advantages to filing second. The party who files first is responsible for drawing up the order or stipulation and that can result in costly legal fees. However, whenever possible a divorce will go much smoother if both parties are on the same page.