This answers an earlier version of the question that was not about the investigative stage.
canada
There is nothing special about an uncorroborated alibi. If the finder of fact (judge or jury) is left with a reasonable doubt about guilt, that calls for an acquittal.
Admissibility of an accused's own testimony does not depend on it being corroborated by a separate witness. See e.g. R. v. L.(J.A.), 2006 MBCA 107:
It is... illogical to argue that an accused’s denial of involvement in a crime is to be treated as non-existent if that denial is provided in the context of an uncorroborated alibi.
Here are standard jury instructions relating to an accused's alibi evidence (R. v. W.(D.), [1991] 1 S.C.R. 742; and R. v. Tomlinson, 2014 ONCA 158, para. 53):
i. ... there is no onus on the accused to prove an alibi;
ii. ... if the jury believes the alibi evidence, they must find the accused not guilty;
iii. ... even if the jury does not believe the alibi evidence, if they are left in a reasonable doubt by it, they must find the accused not guilty; and
iv. ... even if the alibi evidence does not raise a reasonable doubt about an accused’s guilt, the jury must determine, on the basis of all the evidence, whether Crown counsel has proven the guilt of the accused beyond a reasonable doubt.
You talk about a disbelieved alibi as "leading to additional suspicion falling on them." That would be a legal error. See R. v. Hibbert, 2002 SCC 39, para. 62:
Even if an alibi is advanced by the accused himself and is rejected, the finding that the alibi is untrue cannot serve to corroborate or complement the case for the prosecution, let alone permit an inference that the accused is guilty.