i like a girl that is 24 and i am 16 is it illegal for us to have sexual realtions?

The age at which you may legally consent to sexual intercourse in New Hampshire is 16. The sexual offense laws are outlined below.

TITLE LXII CRIMINAL CODE CHAPTER 632-A SEXUAL ASSAULT AND RELATED OFFENSES

Section 632-A:4
632-A:4 Sexual Assault.
I. A person is guilty of a class A misdemeanor under any of the following circumstances:
(a) When the actor subjects another person who is 13 years of age or older to sexual contact under any of the circumstances named in RSA 632-A:2.
(b) When the actor subjects another person, other than the actor's legal spouse, who is 13 years of age or older and under 16 years of age to sexual contact where the age difference between the actor and the other person is 5 years or more.
(c) In the absence of any of the circumstances set forth in RSA 632-A:2, when the actor engages in sexual penetration with a person, other than the actor's legal spouse, who is 13 years of age or older and under 16 years of age where the age difference between the actor and the other person is 3 years or less.
II. A person found guilty under subparagraph I(c) of this section shall not be required to register as a sexual offender under RSA 651-B.
III. A person is guilty of a misdemeanor if such person engages in sexual contact or sexual penetration with another person when the actor is in a position of authority over the person under any of the following circumstances:
(a) When the actor has direct supervisory or disciplinary authority over the victim by virtue of the victim being incarcerated in a correctional institution, the secure psychiatric unit, or juvenile detention facility where the actor is employed; or
(b) When the actor is a probation or parole officer or a juvenile probation and parole officer who has direct supervisory or disciplinary authority over the victim while the victim is on parole or probation or under juvenile probation.
Consent of the victim under any of the circumstances set forth in paragraph III shall not be considered a defense.
Source. 1975, 302:1. 1985, 228:5, eff. Jan. 1, 1986. 2003, 226:5, eff. Jan. 1, 2004; 316:7, eff. Jan. 1, 2004 at 12:01 a.m. 2005, 290:1, eff. Jan. 1, 2006.

TITLE LXII CRIMINAL CODE CHAPTER 632-A SEXUAL ASSAULT AND RELATED OFFENSES

632-A:3 Felonious Sexual Assault. – A person is guilty of a class B felony if such person:
I. Subjects a person to sexual contact and causes serious personal injury to the victim under any of the circumstances named in RSA 632-A:2; or
[Paragraph II effective until January 1, 2007; see also paragraph II set out below.]

II. Engages in sexual penetration with a person other than his legal spouse who is 13 years of age or older and under 16 years of age; or
[Paragraph II effective January 1, 2007; see also paragraph II set out above.]

II. Engages in sexual penetration with a person, other than his legal spouse, who is 13 years of age or older and under 16 years of age where the age difference between the actor and the other person is 3 years or more; or
III. Engages in sexual contact with a person other than his legal spouse who is under 13 years of age.
IV. Engages in sexual contact with the person when the actor is in a position of authority over the person and uses that authority to coerce the victim to submit under any of the following circumstances:
(a) When the actor has direct supervisory or disciplinary authority over the victim by virtue of the victim being incarcerated in a correctional institution, the secure psychiatric unit, or juvenile detention facility where the actor is employed; or
(b) When the actor is a probation or parole officer or a juvenile probation and parole officer who has direct supervisory or disciplinary authority over the victim while the victim is on parole or probation or under juvenile probation.
Consent of the victim under any of the circumstances set forth in paragraph IV shall not be considered a defense.
Source. 1975, 302:1. 1981, 415:4. 1985, 228:4, eff. Jan. 1, 1986. 1997, 220:3, eff. Jan. 1, 1998. 2003, 226:3, 4, eff. Jan. 1, 2004. 2006, 162:1, eff. Jan. 1, 2007