Welcome to the Forum from Virginia;
usually very hard to put a value on family inheritances, simply because the sentimental value is always greater for the Seller, but I have gone to estate sales where the Seller has no interest in either the gun, or the shooting sports, and is not interested in going to auction, or doesn't really have a clue as to current pricing in that particular Model.
With the above said, and assuming you also have no interest for sentimental reasons, and just want to sell it, I would value that gun alone as between $300 to $350, maybe $400 if you are located in one of the "higher price" non gun friendly States.
Below you can see pics of my Model 36 - no dash which is also a 1-7/8" round butt (1965) all original with box, documents and all what we call "the goodies". Sell value around here (central VA) on this 98% package is about $600 in my opinion. My other Model 36 is a dash 1 (1976) with 3" barrel and "J" Frame "target" grips (SB) also all original but no goodies. Sell value right around $500....probably less. These values are what I may be willing to pay if I really wanted either version and from a private seller. Local LGS will offer you considerably a lot less - maybe 40% of Blue Book). None of my Model 36's are rated +P, but yours maybe...check the roll stamp on the right side of the barrel. Looks to me yours is dated pre 2000/2001 (no Internal Lock), but probably mid to late 80's based on triple alpha serial number. I don't have my SCSW 4th with me at work, but someone may come along with a better (closer) date for you.
With yours a potential buyer would need to evaluate first the condition (looks used, but not abused), then the grips, some like rubber, some don't, collectors will deduct the price of J frame non diamond Magna's if RB, more if SB, then any buyer may balk at the "trigger job" regardless of the fact you have a receipt.
Again my opinion only (no disrespect meant) is you could ask $350 on a local site (there are several in each State) and probably get it, but you may get less if someone applies the above deducts. The "big Box" auction sites do eventually settle at "fair market value" but that is sometimes a long way away from "reserve", or "buy-it-now" listed prices, and the seller has to pay the sellers premium, and the buyer has to pay for paperwork, FFL transfer fees and shipping and insurance so most will deduct for that.
I don't believe your gun is in that "rare" or "special" category where you would have collectors and shooters alike in a bidding war.....but only you know that particular guns history and have some provenance to back it up. Was your dad a lawman, or other agency where the gun was his duty gun, or back-up? Do you know if the gun has it's own history known to you or other family members, was it ever part of an incident that was documented?
All these things might mean something to someone who collects and specializes in former police guns and may be willing to pay more for your gun.
There is also the classifieds on this Forum (Want to Buy, Want to Sell) however I am NOT SURE of the RULES on membership and posts before attempting to sell so please address one of the Moderators about the rules, and read them very, very carefully if you decide to post here.
Finally.........please do not take this post wrong. I am not discrediting your gun and any value "guestimate" based solely on photographs is worth basically nothing in lieu of personal hands-on inspection and verification of finish, mechanical integrity.
If you do have (or expect to have in the future) ANY interest in shooting sports, collecting or accumulating firearms, I have to vote with the other posters.....keep it....it was your Dad's, and can NEVER be replaced with another gun....no matter what.
Hope some of the above helps you with your decision and good luck with whatever you decide.
