Well, if you're referring to the crossbow roughly the size of 16th century pistol or smaller (let's say the size of modern handguns), then there is really no proof that such weapon ever existed with few exceptions. We can be pretty sure that the fantasy 'pistol-shaped crossbows' would have been rather unlikely in real life, as the 'pistol grip' gained popularity only in 18th century. Earlier pistol grips were usually pointing away at a slight angle from the line of the barrel.

Ergonomics aside, a crossbow this size would be highly unpractical for any combat use due to the very small battle potential. The 'power' of the crossbow (kinetic energy of the projectile) is generally the product of the mass of the projectile, draw length and draw strength (directly linked to the size and spring characteristics of the bow). The smaller the crossbow, the smaller the bow and lower is the length of the draw would be, as would be the upper limit of the projectile size. So, making an logical assumption that crossbow pistol would have been made using the same material and design of the full-sized crossbow, the smaller version would be inevitably less powerful, thus making it rather useless on the battlefield.

Now, one could as another obvious question - would the small crossbow not be a prime assassin's tool or a holdout self-defense weapon? Well, not really. The main problem with crossbow is that it doesn't really have any good way of retaining the bolt, but there are some ways to alleviate it, so it is not a big drawback. What is really problematic is the fact that the force imparted to the projectile must be fully stored in the drawn bow (unlike in firearms, where force for operating the lock or striker is relatively small and thus easy to contain by a safety mechanism) making the carrying of such loaded weapon extremely dangerous. Furthermore, anything short of modern steel would react rather poorly to the prolonged periods of stress and thus the string and bow of the crossbow often carried in the drawn state would quickly deteriorate.

Now, let's assume that we're not concerned with the longevity of the weapon. Would the small crossbow be still of use? Again, the answer would be negative. Small size of the crossbow and conversely short projectile would mean very short range and penetrative power. Sure, a hit in the major blood vessel or an internal organ could prove fatal, but given that we're speaking of few meters tops, use of such weapon (that would undoubtedly be expensive) makes no practical sense, as in such conditions one could have achieve the same goals with the simple knife, dagger or basically any small pointed object. Of course, there is always a possibility to use a poison, but quick-acting poisons administered via skin penetration were generally unknown in Europe in the heyday of the crossbows and even if they were, contrary to what one sees in the movies, they would give the target plenty of time to retaliate (curare and similar paralytic poisons are used to successfully stalk the gradually weaker and slower prey). If you want to use such weapon in a fantasy setting when there are immediately-acting poisons, feel free to do so but then you should not be concerned with historical or realistic counterparts - that's what fantasy is for.

Now, does all the above mean that there were no small, hand-held crossbows? Not really. There are some specimens of small crossbows. One design of such weapons incorporates a screw mechanism that allows to draw the steel bow by pulling the trigger mechanism attached to the projectile guide (in a design similar to Greek gastraphetes) via rotating the handle. These crossbows are roughly 8-10 inches in length, usually made of metal with the exception of the string. There are few specimens known and they are usually associated with 17th century Italy [1,2] (some people use the name 'ballestrina', a diminutive form of 'ballestra' or crossbow in Italian, although this seems to be modern term, sometimes rendered as 'balestrino', possibly due to confusion with the Italian city of than name). It is almost certain that these were not weapons of any kind but rather expensive toys for the wealthy nobles or patricians who would entertain themselves by shooting targets in gardens or enclosed spaces (not unlike modern airguns) as well as boasting a intricate toy making a great 'conversation piece' . Very high quality of quality of materials and engineering, as well as ornate finish, corroborate the hypothesis of the recreational provenience.

The other form of the small crossbow would be small, usually mostly metal crossbow (often using break-open draw mechanism) used to fire spherical projectiles, usually made of lead. There is quite a few specimens remaining and they usually date back to 17th and 18th century, where they were quite commonly used for target practice or bird hunting [3], especially by younger people only learning to use proper weapons. Sure, this device could still have been dangerous to a human, but even at the very short range it wouldn't have been lethal. Furthermore this hunting weapon can hardly be called a 'hand crossbow' as despite small dimensions it still requires two hands to properly use it.

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[1] Italian hand crossbow, 17th-18th century Italy, from the collection of Metropolitan Museum of Art, New York, USA.
https://www.metmuseum.org/art/collection/search/27510

[2] Hand crossbow, considered of Italian manufacturing and dated late 17th century, sold at Christie's Auction House in London, UK.
https://www.christies.com/LotFinder/lot_details.aspx?from=searchresults&intObjectID=4204177&sid=90568c80-c1bd-4eed-8de5-c4c8cee01523

[3] 'Kugelschnepper' or 'pellet thrower', dated 17th century, from the collection at Schloss Burg near Solingen, Germany.
https://imgur.com/a/4yRx8ZX

So I'm a bit confused. Are you asking whether these things actually existed, or if it's simply possible that someone in a fantasy universe could build one? If it's the latter, I'm not sure you really need our input; it's your imagination and you can do with it as you wish.