LAPD Dog Shooting Family Slams 'Recklessness' of LAPD Officer Who Killed Doodle

The family of the doodle Jameson, who was shot to death by an LAPD officer last Saturday, has torn the "reckless" officer apart after bodycam footage showed them shooting the pup multiple times ... even after he was down.

Jameson's owners, Marie Marseille and Jeremiah Garcia, called the incident "unnecessary and profoundly dangerous" via their attorney, Brett Greenfield ... and questioned the judgement of the officer in a statement to TMZ.

They slammed ... "Throughout the encounter, the officer repeatedly used profanity, focused on the dog’s size, and displayed an aggressive attitude during what was supposed to be a welfare check."

They continued, "The video raises a disturbing question: whether the decision to use deadly force had already been made before any meaningful effort was undertaken to objectively assess the situation, de-escalate the encounter, create distance, or consider alternatives."

The distraught family went on to describe the officer's actions as "escalation" and "recklessness."

We've been following the heartbreaking case -- Marie's neighbor called the cops for a welfare check after she was heard screaming from her apartment, and it was later discovered she was celebrating the Knicks' NBA Championship victory. During Marie's encounter with police, Jameson was shot to death ... with the LAPD claiming Jameson charged at them after Marie was ordered to keep him under control.

But, the family pleads the bodycam footage of the incident shows otherwise, noting to TMZ via Attorney Greenfield... "The footage further appears to show that Jameson was not presenting the type of immediate threat that would justify the rapid escalation that followed."

Mayor Bass called for a "thorough and transparent" investigation, while LAPD Chief McDonnell promised a multilevel, transparent examination of the tragedy.

Greenfield told TMZ the family will sue if things aren't handled "appropriately," telling us ... "I wants them to take accountability. I want them to admit what they did was unjustifiable."

TMZ spoke to the family directly this week, and we were told no apology has been issued. However, the neighbor who called the cops did send their apologies Marie's way.

The investigation is still underway.