When a suspect is arrested and interrogated by the police about a criminal offence, do the police in the states tape record the interview?
Looking at shows like Law & Order SVU which is supposed to be New York, there never is an indication that the interviews are recorded.
Are you guessing or do you know this as a fact? Police did not start routinely tape recording interviews in the UK until the 1980s. When did they start doing it in the states - if it is done routinely? What federal legislation made this compulsory?
They record all of the interviews of suspects. Otherwise the suspect could claim the police forced him to say he did it. Also any lapse in time between the logs and the video would be grounds for a mistrial.
The links that cire provided are for the most part based on a particular state.
I have absolutely no clue what the answer is for any particular region / state of the US. Your best bet would be to contact an authoritative representative of a particular state and ask them the question. Of course, a skilled lawyer would probably be able to prove otherwise in court, but enough of my most-money-always-wins conspiracy theories.
[edit: Why would a person ask (or answer) this question without doing some cursory research?]
My cursory research was the criminology class I had my senior year of high school (1999 - 2000). In the class we were taught that it was customary for police to record a prime suspect(s) to maintain the chain of evidence. In 14 years, since so many police departments have had such issues, I had assumed they all would have adopted that policy by now.
Since it happened in 1990-1991, I don't know if they recorded the confession, but the police caught the three men that murdered my father because the driver turned them all in.
Fun fact is that my Criminology class was taught by the same teacher that taught the Government class, who has been a lawyer since 1985 and at that time was a member of the Sheriff's department. We used to always joke and say, if he snapped he could make your death the perfect crime.