I'm playing a rogue, and cannot find the definitive answer to this question anywhere. I know all about the bonus action nature of the offhand attack, so that is not part of this question. I only want to know if you are required to roll to hit for the offhand attack if you choose to take that bonus action. To me, the PHB is very unclear about this and does not say either way; it only says take your bonus action. Personally, I feel that it makes sense that you don't have to roll for the offhand attack, because the damage is lessened. My DM is kind of leaving it up to me to find the correct answer, and I want to follow the rules properly, so I'm asking here. Thanks.
PHB pg. 194 - You are making an attack, so you need to roll.
First, Two-Weapon fighting. PHB pg. 195, emphasis mine.
When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative. If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.
The process of making an attack is located right before that:
1. Choose a target. Pick a target within your attack’s range: a creature, an object, or a location.
2. Determine modifiers. The DM determines whether the target has cover and whether you have advantage or disadvantage against the target. In addition, spells, special abilities, and other effects can apply penalties or bonuses to your attack roll.
3. Resolve the attack. You make the attack roll. On a hit, you roll damage, unless the particular attack has rules that specify otherwise. Some attacks cause special effects in addition to or instead of damage.
If there’s ever any question whether something you’re doing counts as an attack, the rule is simple: if you’re making an attack roll, you’re making an attack.
The rule for Two-Weapon Fighting states:
When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand.
When you attack, you follow the rules laid out in the Making An Attack section. This includes making an attack roll to see if you hit or miss. If you just did damage, the rule would say you can use your bonus action to score a hit, or something to that effect. The rule even uses the same verb ("attack with...") for both your normal attack the bonus action attack so there's no reason to think the bonus action works any differently, other than not adding your ability modifier to the damage roll.
Note that the damage is not always lessened: Fighters and Rangers can deal full damage if they pick the Two-Weapon Fighting fighting style.