Just FYI, CDOT is probably the worst agency in Colorado when it comes to "consistent" radio usage practices. And yes, they do a fair amount of patching, albeit not quite to the same extent as CSP. For starters, there is no such thing as a "CDOT dispatch center", or even a dedicated CDOT "dispatcher", at least not in the normal sense of the term.
Yes, there are numerous Dispatch Consoles throughout Colorado linked to hundreds, if not several thousand, CDOT DTRS radios programmed with many, many CDOT talkgroups used throughout Colorado. However, there is virtually no consistency in anything CDOT does. A lot of this may be due to either (1) lack of resources, or (2) improper utilization of resources, or perhaps both.
State Patrol's Denver Dispatch center frequently acts as the "primary" dispatcher for CDOT-related calls in the Denver Metro Area. However, CSP has no authority to "order" CDOT employees to do anything, they can only make "requests" (at least that's my impression based on a lot of listening). And, during bad weather or huge traffic backups, many agencies ask CSP to immediately dispatch CDOT trucks to various locations, and CSP in turn relays a massive amount of "requests" to CDOT, often far in excess of what they seemingly are able to handle.
It's also my impression CDOT employees either (a) receive virtually no training whatsoever in radio usage practices, and/or (b) have very, very little interest in following any identifiable "protocol" for radio usage. For example, you will NEVER hear a CDOT truck announce their call sign and associated vehicle number or employee ID number at the beginning of a shift. AFAIK, no dispatcher has a dispatch screen which shows CDOT Employee John Smith assigned to Truck No. XYZ and Radio ID ABC in Area D for Shift 2. Presumably, this might stem from the fact that there is no "in-house" CDOT dispatcher who regularly "dispatches" CDOT trucks to particular calls, and thus they have no particular need to follow any "official" radio usage practices.
Frequently you will hear a frustrated CSP dispatcher flipping through 4-8 CDOT radio channels looking for ANY CDOT truck; when they finally raise someone, half the time the CDOT truck who finally answers insists they are not in the relevant CDOT "area", and instruct the dispatcher to switch to another radio channel that nobody seems to be monitoring. CDOT does have an internal "area" assignment system, but AFAIK it's not fully documented in any publicly-available document/publication (assuming such a publication exists at all, which I've come to doubt). I've previously heard CSP Dispatchers themselves complaining about not having accurate maps of the various CDOT "areas". Again, however, even if you had "official" documentation/maps about the relationship between regions, areas and radio call signs, it may be of limited utility given the (seemingly perpetual) lack of consistency in CDOT's resource allocation practices.
All that being said, you can learn a lot from the maps Spitfire referenced, but there are still gaps which can only be filled by careful monitoring.
Also, it can be difficult to discern the proper alga tag for a particular CDOT talkgroup; Aside from patching, you don't always know whether the CDOT unit claiming to be talking on Channel X is actually transmitting on the TG assigned by the radio shop as Talkgroup X, or if they are "mistakenly" talking on Talkgroup Y. And again, because there is no regular in-house CDOT dispatcher, you will rarely (if ever) hear any dispatcher announce that someone is talking on the wrong channel, and to instruct units to switch to the "correct" channel.
Actually, I suppose there is an "exception" to this: a few months ago, a CDOT employee somehow was using a Radio programmed with a CSP 1-Adam dispatch talkgroup (arguably the first mistake), and said CDOT employee (1) mistakenly had their radio set to a CSP dispatch channel which they had no reason to ever use, and (2) left their radio mic open on that channel for at least 15 minutes. As I recall, they couldn't get ahold of the CDOT employee with the open mic, and they had to actually disable to the radio in question, in order to resume normal traffic on that channel.