I am an (Australian) criminal lawyer. There is no one-size-fits-all answer to the question. As noted by psychonaut, the position in England since the Criminal Justice Act is different from elsewhere. As all lawyers on these boards regularly say, “What jurisdiction are you in?” is fundamental to answering almost any legal question.
In my jurisdiction, the police are equipped with machinery at police stations for the purposes of formal interviews, which simultaneously creates a video and three audio copies of the interview. One of the audio copies is given to the suspect.
So far so good. From the point of view of the suspect, however, not all conversation with the police occurs at the police station. Police commonly have field tape recorders on when they have any conversation with the suspect at the scene, at the arrest, in the police car on the trip to the station, etc. This, however, is subject to local privacy laws - your jurisdictions mileage may differ. The suspect may not know about the field recorder, and suspects frequently contradict themselves in different conversations. The rules about which of the conversations are admissible, so as to allow the contradiction to emerge, are immensely complicated.
Further, if the offence is serious enough, the suspect is arrested and taken to a watchhouse. There, all their property is taken from them, the details entered into a property register, and the property kept (hopefully) safely for them until they are released. The watchhouse keeper is independent of the investigation. That would be the fate of any tape you made of the interview - you would be separated from it.
Though it pains me to say it, it is also necessary to take into account the possibility that the police might lie about what they or you said, pretending that the field tape didn’t work, or they didn’t have one, etc. Thus, they can claim to have warned you earlier than they in fact did, and so on. In my experience this is not in truth common, but is commonly alleged.
Those considerations are more likely to be problematic than maintaining the integrity of what you did say. It is very difficult to edit tapes or other sound recordings undetectably without highly specialist knowledge, and for the police, the stakes are high if they try to dishonestly edit a tape but fail for some reason (of which they are unaware in advance) to do so undetectably. There are various technical steps put in place to prevent that happening.
Claims that police have done so usually come across looking like tin-foil hat stuff. Police are very good witnesses, and likely to come across as the voice of sweet reason. (Suspect: “I wanted to tape the conversation, and you threatened me and smashed my tape recorder, and then undetectably edited the tapes to make it sound like I was confessing when I wasn’t…!” Police officer (rolls eyes): “Now why would I do that? I have no idea how to edit tapes undetectably, and since I was taping, what harm would there have been in letting you tape too?”) Where accounts are likely to differ is in things that are claimed to have been said in the inevitable little bits of conversation that someone or other says were said off-tape. Just who is telling the truth about such matters can only be assessed on a case by case basis. No doubt police sometimes have a motive to invent conversations which never occurred, but that doesn’t mean they have actually done so every time it suits a suspect to say they have. And just because a suspect has an interest in inventing police malfeasance doesn’t mean that he/she is not telling the truth.
Lastly, it is impossible to say in advance whether it is better to talk to the police or decline to do so. Any general policy of that nature is subject to the exigency of the particular case at hand, and while experienced lawyers may have a general inclination one way or another, that is subject to the circumstances as they immediately present themselves. Experienced lawyers know that you can tell a jury till you are blue in the face that no adverse inference is to be drawn from the fact that the suspect declined to be interviewed, and the jury will still say “Yeah, right.” It is easy to imagine circumstances (and I have seen them commonly enough) when a person should have shouted their innocence from the rooftops if they were in truth innocent. If they had told their story early, and had it confirmed by police before there was an opportunity for them to have nobbled witnesses or rearranged physical evidence, that might have been of compelling assistance and prevented later allegations that they left the police station without speaking and then engineered all this exculpatory stuff.
For me, the best policy is to insist politely on contacting a lawyer, and be bloody sure that the lawyer is both experienced and very well resepected. Then take their advice about whether to speak.
