It is fine to write and ask. Do not ask for a specific class of relic. It is very rare for a first class relic to be given to a lay person; which is why the relics with documents and even the ones without on ebay and at other biddings go for very high donations. Usually a priest can write and ask though and receive one. A first class relic is a body part or an actual part of the body of the saint.
A second class relic is something that has touched the saint. Clothing. Tomb. Cloth. Sacramentals. Bed and furniture used by the saint.Things owned by the saint.
A third class relic is something that has touched a second class relic.
A third class relic can be sold, and it is very easy to get one. You can write and they will very likely send you one. A second class relic you might get… you never know. Sometimes they cut up the saints clothes, which supplies tons and tons of relics.
If it is a first or second class… it will come with a document stating it is a true relic of the saint.