Typical appraisal practice does not include verifying permits. In my 25+yrs of appraising, I maybe pulled permits for an appraisal assignment once or twice, but I don't remember the specific circumstances, and I used a service that gets copies of them, and I would charge the client. I have read in appraisal message boards, that in some areas, it may be more common to look for permits, but that is a rarity. I have had many homeowners provide me permits, for work that was done. So, if you want to assure that I will count everything I observe during my inspection, it is up to you, (the homeowner) to provide me with permits.
This usually is an issue, when public records (Assessor records) don't match with the actual improvements. Like in your situation, on record it is a 3/2, but in actuality it is a 4/3. This can happen due to the Assessor not updating the records when additions are done, or when an unpermitted (illegal) addition/alteration is done.
Although, I believe my experience is typical, I am speaking from my personal experience and knowledge in my market areas. All my areas require permits for most alterations, my understanding is that some areas may not require permits.
Also from my experience/areas, just because public records (Assessor) does not have the correct property data, does not mean that it is not legal. The Assessor is separate from Building/Planning department and they may not fully communicate with one another. I was a deputy assessor at the beginning of my career, so I know how this works firsthand. We would only get a small portion of permit information, and it may be the part the states some interior remodeling was done or something that didn't require an onsite inspection to update our files. So, there might've been more info unseen, which related to an addition, or some other significant alteration to the improvements. Therefore, the Assessor records would not get updated and would not accurately reflect the current state of some properties. This also happened a lot in new tracts, where we would just walk down the street and note which lots had which models, but we might miss certain options on a model, like a 4th bedroom option upstairs or a 3rd bathroom or powder room, or something at the rear of the property we can see from the street, etc.
But, the reverse is true also. At the Assessor, I was taught to measure and record the property as I see it, during an inspection. Meaning, I would measure the house at 3,000sf, and note it has 4 bedrooms/3 bathrooms, even if it was a legally permitted 2,000sf 3/2. But, that 1,000sf, 1/1 addition may not be legal, but I may not check, if I am just updating the Assessor role. Then, it was up to the homeowner to go to the Assessor and dispute any potential value increase, due to illegal additions.
So bottom line is ALWAYS VERIFY permit info on any property you buy, especially, if you find any discrepancies.
As an Appraiser, if I am unsure if an addition or another part of an improvement (conversion, etc) is permitted (legal), then I may not give it value and explain, leaving it up to the homeowner to prove it is legal, or I may include it and explain, by using an "extraordinary assumption (EA)." By doing that I am basically saying, I assuming something is true, but if it isn't true, then my conclusions could change. In other words, I assume everything is legally permitted, but if I find out it isn't, my final value estimate may change. Then, the Lender (my client), may request permits or something else from the homeowner (borrower). But, what the EA does is covers me.
Now, just because an area does not have permits, doesn't mean it lacks value. But, that said, typically, it would have less value to a buyer than if it was legally permitted. And, as an Appraiser, it is practically impossible for me to accurately discern the market value of an unpermitted addition, which is why I would most likely use an EA and assume it is legal.
So, after all that, I could've just answered your question with: "YES, either verify there are permits for the additional addition/bedroom/baths, etc, or get permits for those areas that need them." But, keep in mind make sure to get the permits FINALED! Just because you pull a permit, doesn't mean those areas are "permitted." They need to be inspected and APPROVED (signed off)! I have had multiple appraisals where certain work was never signed off and therefore, it was still not fully permitted. And make sure to get a C of O (Certificate of Occupancy) if required in your jurisdiction.
SIDE NOTE:
The Lender's Appraiser can talk to you all they want, what they can't do is discuss their opinions, but they discuss facts. So, they can tell you what the final measurements of the house was, etc, but they can't discuss their value conclusions or how they got there. Unless the client (the Lender) expressly gives permission to speak with the appraiser - which doesn't happen.
AND the Lender can speak with the appraiser directly, they just can't influence them and if they are an originator of the loan, etc, they can't pick the appraiser, etc. Basically, if they will benefit from the loan closing, they can't influence the appraiser or discuss opinions.
....ok, my fingers are tired, hopefully this helps someone...