Seems like a very tricky question. Here is the text of the law with the relevant portion highlighted:
IC 34-28-8
Chapter 8. Disclosure of Firearm or Ammunition Information as a Condition of Employment
IC 34-28-8-1
"Firearm"
Sec. 1. As used in this chapter, "firearm" has the meaning set forth in IC 35-47-1-5.
As added by P.L.17-2011, SEC.2.
IC 34-28-8-2
"Political subdivision"
Sec. 2. As used in this chapter, "political subdivision" has the meaning set forth in IC 36-1-2-13.
As added by P.L.17-2011, SEC.2.
IC 34-28-8-3
"Private employer"
Sec. 3. As used in this chapter, "private employer" means:
(1) an individual;
(2) a partnership;
(3) a firm;
(4) an association;
(5) a corporation; or
(6) a nonprofit organization;
that employs or offers to employ one (1) or more individuals in Indiana.
As added by P.L.17-2011, SEC.2.
IC 34-28-8-4
"Public employer"
Sec. 4. As used in this chapter, "public employer" means:
(1) the state; or
(2) a political subdivision;
including, but not limited to, a department, agency, board, commission, institution, authority, or instrumentality of the state or a political subdivision.
As added by P.L.17-2011, SEC.2.
IC 34-28-8-5
"Public official"
Sec. 5. As used in this chapter, "public official" means an elected or appointed official in the executive, legislative, or judicial branch of the state or a political subdivision, as well as an individual acting on behalf of a public employer, whether temporarily or permanently, including but not limited to, members of boards, committees, commissions, authorities, and other instrumentalities of the state or a political subdivision.
As added by P.L.17-2011, SEC.2.
IC 34-28-8-6
Disclosure of firearm or ammunition information to employer or potential employer
Sec. 6. A public or private employer doing business in Indiana may not:
(1) require an applicant for employment or an employee to disclose information about whether the applicant or employee owns, possesses, uses, or transports a firearm or ammunition, unless the disclosure concerns the possession, use, or transportation of a firearm or ammunition that is used in fulfilling the duties of the employment of the individual; or
(2) condition employment, or any rights, benefits, privileges, or opportunities offered by the employment, upon an agreement that the applicant for employment or the employee forego the:
(A) rights of the applicant or employee under this chapter; or
(B) otherwise lawful:
(i) ownership;
(ii) possession;
(iii) storage;
(iv) transportation; or
(v) use;
of a firearm or ammunition.
As added by P.L.17-2011, SEC.2.
IC 34-28-8-7
Civil action by employee or potential employee authorized when required to divulge firearm or ammunition information
Sec. 7. (a) An individual aggrieved by what the individual believes is a violation of section 6 of this chapter may bring a civil action in a court with jurisdiction against a public or private employer or a public official that is alleged to have violated section 6 of this chapter.
(b) If a person is found by a court in an action brought under subsection (a) to have violated section 6 of this chapter, the court may do the following:
(1) Award:
(A) actual damages;
(B) court costs and attorney's fees; and
(C) in the case of a knowing and willful violation, exemplary or punitive damages;
to the prevailing plaintiff.
(2) Enjoin further violations of this chapter.
As added by P.L.17-2011, SEC.2.
IC 34-28-8-8
Tort claim exception; when not allowed
Sec. 8. IC 34-13-3 does not apply whenever:
(1) a public employer or public official is sued for civil damages; and
(2) the civil action arises out of a violation of section 6 of this
chapter.
As added by P.L.17-2011, SEC.2.
IC 34-28-8-9
Regulation or prohibition of firearm possession or carrying a firearm by employee; when authorized
Sec. 9. Notwithstanding section 6 of this chapter, this chapter does not prohibit a public or private employer from:
(1) regulating or prohibiting the possession or carrying of a firearm by an employee during and in the course of the duties of the employee on behalf of the employer or while on the property of the employer; or
(2) enforcing a regulation or prohibition adopted under subdivision (1).
However, a regulation or prohibition adopted under subdivision (1) may not apply to a firearm stored or transported in accordance with IC 34-28-7.
As added by P.L.17-2011, SEC.2.
The way I read it, the first part I put in bold says that the employer may not ask if you have a firearm in your car, even on company property.
The second part that I put in bold says that if you believe you have a grievance you may bring a "civil action" (this means lawsuit) and if you win you may receive actual damages (lost wages, etc), court and attorney's fees, and punitive damages if the violation was knowing and willful. The third part is very difficult to prove. So is the first part, unless they terminate you and give you a letter that says they fired you because you told them you keep a firearm in the car. If they know you have a firearm in your car and they fire you because you're a lazy employee, you have no case.
The third section I put in bold gives exceptions, such as the prohibition of carrying firearms while you are actually engaged in working for them.
That's just my reading.
You might contact Guy Relford, Esq. in Indianapolis for actual legal advice. I believe has litigated under this chapter as well as under 35-47-11.1.
PM me if you need more info.