It is my understanding that an act of necrophilia with a dead animal or a dead human would be subject to the same general rules under Jewish Law.
IOW, there is no difference if the OP asked about an animal, or a person prohibited to them such as a neighbor's wife, a sibling etc.,
Source #1: Throughout the Torah (for instance Levitivus 18:20, "You shall not lie carnally with your neighbor's wife, to become defiled by her." ) a Hebrew term is used which is loosely translated as "lie carnally" - לֹֽא־תִתֵּ֥ן שְׁכָבְתְּךָ֖ לְזָ֑רַע.
"Do not give your laying down for giving seed.." would be more of a literal translation.
The Talmud in Yevamot 55b explains that this special terminology can only apply when the woman is alive. Intimate sowing of seed, cannot apply to a dead person.
(The Talmud did not simply assume that upon death, the married woman ceases from being a "wife", so that should exclude her from being the object of a prohibition; as the Talmud continues:
" Rather, according to this opinion, the verse excludes one who has intercourse with a dead woman. As it might enter your mind to say: Since after death she is also called "her husband’s kin" ("She-ey-ro"), say that one who had intercourse with her should be liable to receive punishment for committing adultery with a married woman. It therefore teaches us that intercourse with a dead woman is not considered intercourse at all.")(Sefaria online version)
See Rashi on this Gemara who refers to Leviticus 21:2. The word "She-ey-ro there means close relative and Rashi on this verse identifies the term as referring to the Kohen's wife who has died; see also Yevamos 22b and Toras Kohanim 21:5. Thanks to The GRAPKE for asking about this.)
Therefore, the Talmud concludes that there is no Torah prohibition for an act of necrophilia upon a neighbor's wife, since the woman has already died.
Source #2: Deutoronomy 22:22 "If a man is found lying with a married woman, even both of them shall die; the man lying with the woman and the woman. So shall you clear away the evil from Israel."
The Talmud in Sanhedrin 66b explains that the Torah teaches here that the term "both of them shall die" comes to say that there must be a special case where one person cannot be found guilty because the other partner to the intercourse, is not liable for this act.
Rashi and Tosafot recognize that there is an opinion mentioned in some versions of the Talmud that the case of exemption taught would be "The act of Herod"
"The act of Herod" is necrophilia as can be seen by looking at the Talmud
in Baba Basra 3b: "It is related that Herod preserved the girl’s body in honey for seven years to prevent it from decaying. There are those who say that he engaged in necrophilia with her corpse and there are those who say he did not engage in necrophilia with her corpse. According to those who say he engaged in necrophilia with her corpse, the reason that he preserved her body was to gratify his carnal desires. And according to those who say he did not engage in necrophilia with her corpse, the reason that he preserved her body was so that people would say he married a king’s daughter." (Translation from Sefaria online)
Therefore, the Talmud has one opinion that from the terminology in this verse (Deut. 22:22), the Torah does not prohibit an act of necrophilia.
The party performing the act of necrophilia upon the corpse cannot be held liable because the "partner" to the act is also not liable in this case (the dead cannot be held liable).
(NOTE: there are other cases where a party can be held liable where the partner is exempt ie: raping a helpless married woman.)
Source #3: However, in Sanhedrin 78a, the talmud discusses the case of a "trey-fah" which is a man who is injured or sick to such an extent, that it is assumed he will shortly, and most certainly, die. Therefore the "trey-fah" is given the Halachic (Jewish Law) status, as someone who is technically already dead, regarding many Halachic considerations.
However, Rava states an exception regarding necrophilia:
Rava explains that although a man who commits an act of sodomy upon another man who has the status of a "trey-fah", should technically be exempt from punishment (as there is no prohibition of sodomy with the dead); Still, since the offender had pleasure from the act, and the other person was technically alive with all the physical characteristics of a living body, then the Torah prohibition applies to obligate the offender in the death penalty for sodomy.
So this Talmudic passage also states that there is no Torah prohibition against necrophilia with a bona-fide corpse.
But what about an animal and if an animal is dead; or between dead and alive status?
Source #4: The Talmud in Chulin 121b, discusses the case of a non-kosher animal slaughtered by a Jew (so he could feed it to his Gentile friend it would seem) that is still thrashing about in its death throes.
Abayye says (that although an act of necrophilia upon a truly dead animal is not liable at all), that in this case, since the animal is still thrashing, the offender would in fact be liable for committing the act of beastiality with this quasi-dead animal.
The Chasam Sofer on Chulin 121b, suggests that for technical reasons, Rava and Abayye may argue vis-a-vis comparing source #3 to #4 etc. (See also Rashash in Chulin as well).
We can conclude by quoting the Rambam Hilchos Issurei Biah, Ch. 1 Halacha 12: (who deals with this issue and finalizes the Law in his opinion)
"When a person enters into sexual relations with one of the arayot as a casual act, although he did not intend to do so, he is liable. Similar concepts apply with regard to one who enters into relations with women forbidden by a negative commandment alone or with one of the shniyot.
When, however, a man has relations with one of the arayot after she died, he is not liable at all. Needless to say, this applies with regard to those women with whom relations are forbidden by a negative commandment alone. When, by contrast, one has relations with a person who is trefe or who has relations with an animal which is trefe, he is liable. [The person or the animal] is [now] alive even though he will ultimately die from this illness. Even when the two signs (in the throat) which validate ritual slaughter were slit but [the woman or the animal] is making its last movements, if one enters into relations with [her or it] he is liable until she or it dies or is decapitated." (Chabad.org English online version)
But besides the above exception about a dying and thrashing animal there is no prohibition in the Torah about necrophilia with a person or animal.
(It would seem there are Rabbinical and ethical prohibitions under Jewish law, and Jewish thought, that may apply; but that is beyond the question of the OP.)
I hope this helps,