Question:
Is it permitted for someone to bury a fetus after a miscarriage in their own backyard?
Answer:
One should not do so. It is forbidden for a kohen to become ritually impure through contact with the dead, which includes a fetus. Therefore, out of precaution for the Kohanim, such cases are typically entrusted to the chevra kadisha to handle, or the remains are buried in a designated area of a local cemetery.
Sources
Regarding burial: Michaber and Rama Y.D. 263:5; O.C. 526:10; Admur 526:19-20; M”A 526:20; Avnei Nezer 472; Pischeiy Teshuvah 357:1; Regarding Tumas Kohanim: Rambam Tumas Meis 2:1; 9:2; 11:7; Bach Y.D. 369; Taz 369:1; Noda Beyehuda Y.D. Kama 97; Chidushei Hagirshoni; Pischeiy Teshuvah 369:2; Kitzur SHU”A 202:1; Nitei Gavriel 130:12; 135:9; Heichal Horah 3:120; 5 p. 113; Encyclopedia Hilchatit Refuit Vol. 3 Erech Yilud p. 928