Short answer
Reasonable and respectful verification is advisable, especially for important claims that affect the marriage decision.
Islamic Guidance
What Islam teaches
Islam emphasizes verification, truthfulness and avoiding suspicion without evidence. Verification should be fair and should not become spying, gossip or unjust character assassination.
Practical Guidance
What you can consider
Verify important information through appropriate sources. Confirm marital status, education, employment and major disclosures without violating privacy or spreading rumors.
Sources
Qur'an 49:6; Qur'an 49:12.