This problem involves analyzing statements made by suspects with known truth-telling or lying tendencies to determine their guilt or innocence and identify which statement is false. We have four suspects: A, B, C, and D. A and D always tell the truth, while B and C always lie. C and D are identical twins, making it tricky to distinguish them initially.

Suspect Analysis and Statement Evaluation

Let's break down the information given:

• A: Truthful
• B: Untruthful (Liar)
• C: Untruthful (Liar)
• D: Truthful

C and D are twins, one truthful (D), one untruthful (C).

Evaluating Individual Statements

1. A says, "D is innocent": Since A is always truthful, this statement is true. Therefore, D is innocent.
2. B says, "A is guilty": Since B is always untruthful, this statement is false. The opposite must be true. Therefore, A is not guilty (A is innocent). This aligns with A being truthful, as a truthful person is unlikely to be the criminal.
3. Among C and D, one says, "A is innocent" and the other says, "B is guilty":
   • We know D is truthful and C is untruthful.
   • We know "A is innocent" is a true statement (from evaluating A's and B's statements).
   • Since D is truthful, D must be the one who says the true statement. Thus, D says, "A is innocent".
   • This leaves C, the untruthful twin, to say the other statement: C says, "B is guilty".
   • Since C is untruthful, C's statement "B is guilty" must be false. The opposite is true: B is not guilty (B is innocent).

Summary of Deductions

Based on the statements and the nature of the suspects, we can deduce the following:

• A is truthful and innocent.
• B is untruthful and innocent.
• D is truthful and innocent.
• C is untruthful. C said "B is guilty" which is a lie. If B is innocent (which we deduced), then C lied. This fits C's nature. Since only one suspect committed the crime, and A, B, and D are innocent, C must be the guilty one.

Let's summarise who is truthful/untruthful, who is innocent/guilty, and what each person said:

Evaluating the Options

We need to find the statement among the options that is FALSE based on our deductions.

1. D said "A is innocent": From our analysis, D (the truthful twin) said "A is innocent". This statement is TRUE.
2. D is innocent: From A's statement and our deductions, D is indeed innocent. This statement is TRUE.
3. B is innocent: From C's lie ("B is guilty"), we deduced that B is innocent. This statement is TRUE.
4. C is innocent: From our deductions, C is the untruthful twin who lied about B, and is the only remaining suspect who could have committed the crime. C is guilty, not innocent. This statement is FALSE.

Therefore, the statement that is FALSE is "C is innocent".