In many but not all common law jurisdictions, a person who comitts an "inherently dangerous" crime can be found guilt of "felony murder" (not manslaughter).
The Wikipedia article says:
In most jurisdictions, to qualify as an underlying offense for a felony murder charge, the underlying offense must present a foreseeable danger to life, and the link between the offense and the death must not be too remote. For example, if the recipient of a forged check has a fatal allergic reaction to the ink, most courts will not hold the forger guilty of murder, as the cause of death is too remote from the criminal act.
Floyd was arrested on an accusation that he passed a counterfeit $20 bill. This is not an "inherently dangerous" felony. Nor has it ever been established that he had the criminal intent that would have been required to convict him of a crime. Indeed it has not been proved that he knew the bill was counterfeit. But a finding of criminal intent to commit the underlying felony is essential to invoking teh felony murder rule. MN code 609.632 subdivision 3 requires "intent to defraud" and "having reason to know that the money order, currency, note, or obligation or security is forged, counterfeited, falsely made, altered, or printed". Moreover when the value is under $1,000 the possible penalties are much lighter and may not even be a felony.
In any case passing a phoney $20 is not the kind of offense for which the felony murder rule is normally invoked, nor is being killed by an arresting officer a plausible, outcome, althoguh obviously it is possible.
The University of Minnesota's page on "felony Murder" says:
When the defendant commits a felony that is inherently dangerous to life, he or she does so knowing that some innocent victim may die. In essence, this awareness is similar to implied malice, knowingly, or recklessly under circumstances manifesting extreme indifference to the value of human life. What is difficult to justify is a conviction for felony murder when the felony is not inherently dangerous to life. Thus most jurisdictions limit the felony murder doctrine to felonies that create a foreseeable risk of violence or death. ...
Joaquin, who has just lost his job, decides to burn down his apartment building because he can’t afford to pay the rent. Joaquin carefully soaks his apartment with lighter fluid, exits into the hallway, and throws a lit, lighter-fluid-soaked towel into the apartment. He then runs outside to watch the entire building burn down. Several tenants die of smoke inhalation because of the fire. In jurisdictions that recognize felony murder, Joaquin can probably be charged with and convicted of murder for every one of these deaths.
In this example, Joaquin did not intend to kill the tenants. However, he did most likely have the criminal intent necessary for arson. Therefore, felony murder convictions are appropriate. Note that Joaquin exhibited extreme indifference to whether the tenants in the building lived or died, which could also constitute the criminal intent of implied malice or depraved heart.
The Minnesota code Section 609.19 MURDER IN THE SECOND DEGREE says:
Subd. 2.Unintentional murders.
Whoever does either of the following is guilty of unintentional murder in the second degree and may be sentenced to imprisonment for not more than 40 years:
(1) causes the death of a human being, without intent to effect the death of any person, while committing or attempting to commit a felony offense other than criminal sexual conduct in the first or second degree with force or violence or a drive-by shooting;
[Paragraph (2) deals with death "while intentionally inflicting or attempting to inflict bodily harm upon the victim" which clearly does not apply in this case.]