Colin Kaepernick, 28, has refused to stand for the national anthem in a protest against the plight of black people in the US.
A letter from Santa Clara police says Colin Kaepernick’s actions and statements are “false and insulting”.
It accused the 49ers of failing to take any action to stop them.
Colin Kaepernick’s protest has stemmed from the racial tensions that increased across the nation this year amid a string of police killings and subsequent revenge attacks.
The quarterback stayed seated during The Star-Spangled Banner at a game a week ago and on Thursday chose to kneel during the anthem.
Colin Kaepernick has said he will continue until he sees improvements in US race relations.
The Santa Clara Police Officers’ Association letter, obtained by NBC Bay Area, said that Colin Kaepernick had “made the allegation that police officers are getting paid to murder people”.
It accused the 49ers of “allowing Kaepernick to wear exposed socks with the image of a pig wearing a police hat”.
The letter said: “The 49ers organization has taken no action to stop or prevent Mr Kaepernick from continuing to make inaccurate, incorrect and inflammatory statements.
“If the 49ers organization fails to take action to stop this type of inappropriate workplace behavior, it could result in officers choosing not to work at your facilities.
“Our members have the right to do their job in an environment free of unjustified and insulting attacks.”
About 70 Santa Clara officers patrol Levi’s Stadium during the home games.
On September 1, Colin Kaepernick vowed to continue his protest, saying: “The message is that we have a lot of issues in this country that we need to deal with.”
Teammate Eric Reid joined him in the latest protest.
Seattle Seahawks player Jeremy Lane also sat on the bench during the anthem at a game in Oakland.
Jeremy Lane later told the News Tribune: “I wasn’t trying to say anything, just standing behind Kaepernick.”
Colin Kaepernick’s anthem protest has drawn strong reactions both in opposition and support.
An online petition demanding the NFL punish Colin Kaepernick attracted more than 53,000 signatures by September 2.
However, some veterans and military members tweeted their support for Colin Kaepernick with the hashtag #VeteransForKaepernick.
The NFL says it encourages players to stand for the anthem but that it is not a requirement.
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